જો cos A = frac{3}{4} , તો 32sin frac{A}{2}cos frac{5}{2}A =

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

easy

જો $\cos A = \frac{3}{4}$, તો $32\sin \frac{A}{2}\cos \frac{5}{2}A = $

A

$\sqrt 7 $

B

$ - \sqrt 7 $

C

$7$

D

$-7$

Solution

(b) $\cos A = \frac{3}{4} \Rightarrow \sin A = \frac{{\sqrt 7 }}{4}$

$L.H.S.$ $ = 16(\sin 3A – \sin 2A)$

$ = 16\sin A(3 – 4{\sin ^2}A – 2\cos A)$

$ = 16.\frac{{\sqrt 7 }}{4}\left( {3 – 4.\frac{7}{{16}} – 2.\frac{3}{4}} \right) = – \sqrt 7 $.

Standard 11

Mathematics

Share

Similar Questions

સાબિત કરો કે : $\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x$

medium

જો $x = \sin {130^o}\,\cos {80^o},\,\,y = \sin \,{80^o}\,\cos \,{130^o},\,\,z = 1 + xy,$ તો આપેલ પૈકી ક્યૂ સત્ય છે.

easy

જો $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right),$ તો $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ ની કિમંત મેળવો.

hard

(IIT-1984)

${\cos ^2}A{(3 – 4{\cos ^2}A)^2} + {\sin ^2}A{(3 – 4{\sin ^2}A)^2} = $

easy

જો $0 < x , y < \pi$ અને $\cos x +\cos y-\cos ( x + y )=\frac{3}{2}$ હોય, તો $\sin x+\cos y =$ …… .

hard

(JEE MAIN-2021)