Question

Find the value of cos 38o x cos 52o − sin 38o x sin 52o​

Answer 1

$\textbf{Given:}$

$\mathsf{cos\,38^\circ\;cos\,52^\circ-sin\,38^\circ\;sin\,52^\circ}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{cos\,38^\circ\;cos\,52^\circ-sin\,38^\circ\;sin\,52^\circ}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{cos\,38^\circ\;cos\,52^\circ-sin\,38^\circ\;sin\,52^\circ}$

$\textsf{Using the identity,}$

$\boxed{\mathsf{cos(A+B)=cosA\;cosB-sinA\;sinB}}$

$\mathsf{=cos(38^\circ+52^\circ)}$

$\mathsf{=cos\,90^\circ}$

$\mathsf{=0}$

$\implies\boxed{\mathsf{cos\,38^\circ\;cos\,52^\circ-sin\,38^\circ\;sin\,52^\circ=0}}$

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Answer 2

SOLUTION

TO DETERMINE

The value

cos 38° × cos 52° - sin 38° × sin 52°

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

cos ( 90° - θ ) = sin θ

EVALUATION

cos 38° × cos 52° - sin 38° × sin 52°

= cos ( 90° - 52° ) × cos ( 90° - 38° ) - sin 38° × sin 52°

= sin 52° × sin 38° - sin 38° × sin 52°

= sin 38° × sin 52° - sin 38° × sin 52°

= 0

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