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Q.

From the following options, find the value of sin 54 ° −cos 36 °  .


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a

sin36°  

b

cos54°  

c

1

d

0 

answer is D.

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Detailed Solution

Given that, sin 54 ° −cos 36 °  .
We know that, the complementary formula for sinθ   is:
sin( 90 ° −θ)=cosθ  
Convert sinθ   into cosθ   trigonometric function.
⇒sin 54 ° −cos 36 ° =sin(90°−36°)−cos36°   Apply complementary angle formula,
⇒sin 54 ° −cos 36 ° =cos 36 ° −cos 36 ° ⇒sin 54 ° −cos 36 ° =0   Thus, sin 54 ° −cos 36 ° =0  .
Hence, option 4) is correct.
 
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