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Category: Trigonometry

if-the-maximum-value-of-4sin-2-x-3cos-2-x-sin-x-2-cos-x-2-3-is-a-b-then-find-a-b-

Question Number 146876 by gsk2684 last updated on 16/Jul/21 $${if}\:{the}\:{maximum}\:{value}\:{of}\: \\ $$$$\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{3cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:\frac{{x}}{\mathrm{2}}+\mathrm{cos}\:\frac{{x}}{\mathrm{2}}+\mathrm{3} \\ $$$${is}\:{a}+\sqrt{{b}}\:{then}\:{find}\:{a}+{b} \\ $$ Answered by liberty last updated on 16/Jul/21…

In-a-triangle-ABC-if-sin-A-5-x-sin-B-3x-1-sin-C-2x-5-then-find-integral-solutions-x-

Question Number 146875 by gsk2684 last updated on 16/Jul/21 $${In}\:{a}\:{triangle}\:{ABC},\:{if}\: \\ $$$$\frac{\mathrm{sin}\:{A}}{\mathrm{5}−{x}}=\frac{\mathrm{sin}\:{B}}{\mathrm{3}{x}−\mathrm{1}}=\frac{\mathrm{sin}\:{C}}{\mathrm{2}{x}+\mathrm{5}}\:{then}\:{find} \\ $$$$\:{integral}\:{solutions}\:{x}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-the-line-joining-through-orthocenter-and-circumcenter-of-a-triangle-ABC-is-parallel-to-the-base-BC-then-find-tan-B-tan-C-

Question Number 146874 by gsk2684 last updated on 16/Jul/21 $${let}\:{the}\:{line}\:{joining}\:{through}\: \\ $$$${orthocenter}\:{and}\:{circumcenter}\: \\ $$$${of}\:{a}\:{triangle}\:{ABC}\:{is}\:{parallel}\:{to}\: \\ $$$${the}\:{base}\:{BC}\:{then}\:{find}\:\:\mathrm{tan}\:{B}.\mathrm{tan}\:{C} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-tan-2-x-sec-x-a-1-has-at-least-one-solution-then-find-the-complete-set-of-values-of-a-

Question Number 146868 by gsk2684 last updated on 16/Jul/21 $${if}\:\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{sec}\:{x}={a}+\mathrm{1}\:{has}\:{at}\:{least}\: \\ $$$${one}\:{solution}\:{then}\:{find}\:{the}\:{complete}\:{set} \\ $$$${of}\:{values}\:{of}\:\:'{a}'? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jul/21 $$\mathrm{tan}^{\mathrm{2}}…

Solve-for-x-cos-x-7-cos-2x-7-cos-3x-7-1-2-

Question Number 15786 by tawa tawa last updated on 13/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{7}}\right)\:−\:\mathrm{cos}\left(\frac{\mathrm{2x}}{\mathrm{7}}\right)\:+\:\mathrm{cos}\left(\frac{\mathrm{3x}}{\mathrm{7}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by tawa tawa last updated on 14/Jun/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this}. \\…

Let-us-call-complex-triangle-which-has-either-sides-or-angles-are-complex-numbers-Let-a-b-c-R-which-are-sides-of-a-complex-triangle-which-need-not-satisfy-triangle-inequality-say-a-1-b-2-and-c-4-P

Question Number 15759 by prakash jain last updated on 13/Jun/17 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{call}\:\mathrm{complex}\:\mathrm{triangle}\:\mathrm{which} \\ $$$$\mathrm{has}\:\mathrm{either}\:\mathrm{sides}\:\mathrm{or}\:\mathrm{angles}\:\mathrm{are} \\ $$$$\mathrm{complex}\:\mathrm{numbers}. \\ $$$$\mathrm{Let}\:{a},{b},{c}\:\in\mathbb{R}\:\mathrm{which}\:\mathrm{are}\:\mathrm{sides}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{complex}\:\mathrm{triangle}\:\mathrm{which}\:\mathrm{need} \\ $$$$\mathrm{not}\:\mathrm{satisfy}\:\mathrm{triangle}\:\mathrm{inequality}. \\ $$$$\mathrm{say}\:{a}=\mathrm{1},{b}=\mathrm{2}\:\mathrm{and}\:{c}=\mathrm{4}. \\ $$$$\mathrm{Prove}\:\left(\mathrm{or}\:\mathrm{counter}\:\mathrm{example}\right)…

If-sides-of-triangle-are-x-2-x-1-2x-1-and-x-2-1-prove-that-greatest-angle-is-120-Also-find-the-range-of-x-such-that-triangle-exist-

Question Number 15760 by Tinkutara last updated on 13/Jun/17 $$\mathrm{If}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{are}\:{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{1}, \\ $$$$\mathrm{2}{x}\:+\:\mathrm{1}\:\mathrm{and}\:{x}^{\mathrm{2}} \:−\:\mathrm{1},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{greatest} \\ $$$$\mathrm{angle}\:\mathrm{is}\:\mathrm{120}°.\:\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{triangle}\:\mathrm{exist}. \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated…

If-in-a-ABC-2-cos-A-a-cos-B-b-2-cos-C-c-a-bc-b-ac-prove-that-A-90-

Question Number 15761 by Tinkutara last updated on 13/Jun/17 $$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\Delta{ABC},\:\frac{\mathrm{2}\:\mathrm{cos}\:{A}}{{a}}\:+\:\frac{\mathrm{cos}\:{B}}{{b}}\:+\:\frac{\mathrm{2}\:\mathrm{cos}\:{C}}{{c}} \\ $$$$=\:\frac{{a}}{{bc}}\:+\:\frac{{b}}{{ac}}\:,\:\mathrm{prove}\:\mathrm{that}\:\angle{A}\:=\:\mathrm{90}°. \\ $$ Answered by ajfour last updated on 13/Jun/17 $$\frac{\mathrm{2cos}\:{A}}{{a}}+\frac{\mathrm{cos}\:{B}}{{b}}+\frac{\mathrm{2cos}\:{C}}{{c}}=\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{{abc}} \\…