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Q.




What is the value of the expression cos 38° ×   cos 52° – sin 38° ×   sin 52° ?

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a

-1

b

1

c

0

d

None of these 

answer is C.

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Detailed Solution

Given expression is cos 38° ×   cos 52° – sin 38° ×   sin 52°.
We know that,
sinx=cos( 90 ∘ −x) cosx=sin( 90 ∘ −x)   The given expression becomes,
⇒cos 38° cos 52°–sin 38°sin 52° ⇒sin 90°− 38° sin 90°− 52°  – sin 38° sin 52° ⇒sin 38°sin 52°–sin 38°sin 52° ⇒0  
The value of the expression cos 38° ×  cos 52° – sin 38° ×  sin 52° is 0.
Therefore, the correct option is 3.
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