Question and Answers Forum

if the sides a,b,c of a triangle ABC are in A.P. and if sin A =(sin B +sin C)cos α sin B =(sin C+sin A)cos β sin C =(sin A +sin B)cos γ then find the value of tan^2 (α/2)+tan^2 (γ/2)

$i f t h e s i d e s a, b, c o f a t r i a n g l e A B C$ $a r e i n A . P . a n d i f$ $\sin A = (\sin B + \sin C) \cos α$ $\sin B = (\sin C + \sin A) \cos β$ $\sin C = (\sin A + \sin B) \cos γ$ $t h e n f i n d t h e v a l u e o f$ $\tan^{2} \frac{α}{2} + \tan^{2} \frac{γ}{2}$

Question Number 146876 Answers: 1 Comments: 0

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

$i f t h e m a x i m u m v a l u e o f$ $4 \sin^{2} x + 3 \cos^{2} x + \sin \frac{x}{2} + \cos \frac{x}{2} + 3$ $i s a + \sqrt{b} t h e n f i n d a + b$

Question Number 146875 Answers: 0 Comments: 0

In a triangle ABC, if ((sin A)/(5−x))=((sin B)/(3x−1))=((sin C)/(2x+5)) then find integral solutions x?

$I n a t r i a n g l e A B C, i f$ $\frac{\sin A}{5 - x} = \frac{\sin B}{3 x - 1} = \frac{\sin C}{2 x + 5} t h e n f i n d$ $i n t e g r a l s o l u t i o n s x ?$

Question Number 146874 Answers: 0 Comments: 0

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

$l e t t h e l i n e j o i n i n g t h r o u g h$ $o r t h o c e n t e r a n d c i r c u m c e n t e r$ $o f a t r i a n g l e A B C i s p a r a l l e l t o$ $t h e b a s e B C t h e n f i n d \tan B . \tan C$

Question Number 146865 Answers: 1 Comments: 0

arcsin(x^2 −4) = arcsin(2x + 4) ⇒ x = ?

$a r c s i n (x^{2} - 4) = a r c s i n (2 x + 4)$ $\Rightarrow x = ?$

Question Number 146866 Answers: 1 Comments: 0

((sin^6 𝛂 + cos^6 𝛂 - 1)/(sin^4 𝛂 - sin^2 𝛂)) = ?

$\frac{{s i n}^{6} α + {c o s}^{6} α - 1}{{s i n}^{4} α - {s i n}^{2} α} = ?$

Question Number 146863 Answers: 1 Comments: 1

Question Number 146910 Answers: 1 Comments: 0

Question Number 146911 Answers: 0 Comments: 0

(dy/dx) = ((2cos^2 x−sin^2 x+y^2 )/(2cos x)) y(0)=−1 & y(1)=sin x

$\frac{dy}{dx} = \frac{2 \cos^{2} x - \sin^{2} x + y^{2}}{2 \cos x}$ $y (0) = - 1 & y (1) = \sin x$

Question Number 147008 Answers: 0 Comments: 1

find the number of values of cot θ where θ∈[(π/(12)) (π/2)] satisfying the equation [tan θ.[cot θ]]=1 ? (where [x] is greatest integer less than or equal to x)

$f i n d t h e n u m b e r o f v a l u e s o f \cot θ$ $w h e r e θ \in [\frac{π}{12} \frac{π}{2}] s a t i s f y i n g t h e$ $e q u a t i o n [\tan θ . [\cot θ]] = 1 ?$ $(w h e r e [x] i s g r e a t e s t i n t e g e r$ $l e s s t h a n o r e q u a l t o x)$

Question Number 147007 Answers: 1 Comments: 0

Question Number 146860 Answers: 2 Comments: 0

∫sin(x) cos(x) dx = ?

$\int s i n (x) c o s (x) d x = ?$

Question Number 146859 Answers: 1 Comments: 0

∫_( 0) ^3 (√((x+2)^2 −8x)) = ?

$\underset{0}{\int^{3}} \sqrt{{(x + 2)}^{2} - 8 x} = ?$

Question Number 146854 Answers: 1 Comments: 2

Solve for real numbers the following system of equations { ((a(a+1) = b−1)),((a^2 (b+3)+2a = −1)) :}

$S o l v e f o r r e a l n u m b e r s t h e f o l l o w i n g$ $s y s t e m o f e q u a t i o n s$ ${\begin{cases} a (a + 1) = b - 1 \\ a^{2} (b + 3) + 2 a = - 1 \end{cases}$

Question Number 146853 Answers: 0 Comments: 0

Question Number 146850 Answers: 0 Comments: 0

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