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Category: Trigonometry

Question-116290

Question Number 116290 by ravisoni last updated on 02/Oct/20 Commented by Dwaipayan Shikari last updated on 03/Oct/20 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{−\mathrm{1}} \mathrm{x} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)=\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{−\frac{\mathrm{1}}{\mathrm{2}}}…

Prove-that-sin-10-sin-30-sin-50-sin-70-

Question Number 116281 by aye48 last updated on 02/Oct/20 $$\mathrm{Prove}\:\mathrm{that}\:\:\:\mathrm{sin}\:\mathrm{10}°\:\mathrm{sin}\:\mathrm{30}°\:\mathrm{sin}\:\mathrm{50}°\:\mathrm{sin}\:\mathrm{70}°. \\ $$ Answered by Dwaipayan Shikari last updated on 02/Oct/20 $$\mathrm{sin}\theta\mathrm{sin3}\theta\mathrm{sin5}\theta\mathrm{sin7}\theta\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\theta=\mathrm{10}° \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2sin}\theta\mathrm{sin7}\theta\right)\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2sin5}\theta\mathrm{sin3}\theta\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{cos6}\theta−\mathrm{cos8}\theta\right)\left(\mathrm{cos2}\theta−\mathrm{cos8}\theta\right)…

If-cos-2y-tan-2-x-prove-that-cos2x-tan-2-y-

Question Number 50705 by 786786AM last updated on 19/Dec/18 $$\mathrm{If}\:\mathrm{cos}\:\mathrm{2y}\:=\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{cos2x}=\mathrm{tan}\:^{\mathrm{2}} \mathrm{y}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 19/Dec/18 $${cos}\mathrm{2}{x} \\ $$$$=\frac{\mathrm{1}−{tan}^{\mathrm{2}} {x}}{\mathrm{1}+{tan}^{\mathrm{2}}…

prove-that-1-cos0-cos1-1-cos1-cos2-1-cos88-cos89-cos1-sin-2-1-

Question Number 181592 by mathlove last updated on 27/Nov/22 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{cos}\mathrm{0}\:{cos}\mathrm{1}\:}+\frac{\mathrm{1}}{{cos}\mathrm{1}\:{cos}\mathrm{2}}+……+\frac{\mathrm{1}}{{cos}\mathrm{88}\:{cos}\mathrm{89}}=\frac{{cos}\mathrm{1}}{{sin}^{\mathrm{2}} \mathrm{1}} \\ $$ Answered by som(math1967) last updated on 27/Nov/22 $$\frac{\mathrm{1}}{{sin}\mathrm{1}}\left[\frac{{sin}\left(\mathrm{1}−\mathrm{0}\right)}{{cos}\mathrm{0}{cos}\mathrm{1}}+\frac{{sin}\left(\mathrm{2}−\mathrm{1}\right)}{{cos}\mathrm{1}{cos}\mathrm{2}}+\right. \\ $$$$\left….+\frac{{sin}\left(\mathrm{89}−\mathrm{88}\right)}{{cos}\mathrm{88}{cos}\mathrm{89}}\right]…

Find-the-sum-to-n-terms-of-the-series-1-x-a-1-x-x-2-a-2-1-x-x-2-x-3-a-3-1-x-x-2-x-3-

Question Number 116023 by aye48 last updated on 30/Sep/20 $$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{x}}{\mathrm{a}}\:\left(\mathrm{1}\:+\:\mathrm{x}\right)+\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \right)+\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{a}^{\mathrm{3}} }\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \right)\:+\:\ldots \\ $$$$ \\ $$ Answered by…