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Q.

If sin3A=cos A− 26 ° ,   where 3A   is an acute angle, find the value of A   from the following choices.


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a

17°  

b

29°  

c

38°  

d

45°   

answer is B.

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Detailed Solution

Given that, sin3A=cos A− 26 °  .
Write complementary angle formula for sinθ,cosθ  .
We know that, sinθ=cos( 90 ° −θ)  .
sin3A=cos A− 26 o  
or cos( 90 ° −3A)=cos A− 26 o  .
Cancel cosine from both sides,
⇒ 90 ° −3A=A−26° ⇒4A=116° ⇒A=29°  
The value of A is 29°  .
Hence, option 2) is correct.
 
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If sin3A=cos A− 26 ° ,   where 3A   is an acute angle, find the value of A   from the following choices.