Solveeit Logo
Login

Question

Question: If \(\cos A = \frac{3}{4}\), then \(32\sin\frac{A}{2}\cos\frac{5}{2}A =\)...

If cos⁡A=34\cos A = \frac{3}{4}, then 32sin⁡A2cos⁡52A=32\sin\frac{A}{2}\cos\frac{5}{2}A =

A

7\sqrt{7}

B

−7- \sqrt{7}

C

7

D

–7

Answer

−7- \sqrt{7}

Explanation

Solution

cos⁡A=34⇒sin⁡A=74\cos A = \frac{3}{4} \Rightarrow \sin A = \frac{\sqrt{7}}{4}

L.H.S =16(sin⁡3A−sin⁡2A)= 16(\sin 3A - \sin 2A)

=16sin⁡A(3−4sin⁡2A−2cos⁡A)= 16\sin A(3 - 4\sin^{2}A - 2\cos A)

=16.74(3−4.716−2.34)=−7= 16.\frac{\sqrt{7}}{4}\left( 3 - 4.\frac{7}{16} - 2.\frac{3}{4} \right) = - \sqrt{7}.