Question

3. If A = 15°, find the value of :
cos 3A-2cos 4A
sin3A+2sin 4A​

Answer 1

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If A = 15°

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A. T. Q

Cos 3A - 2cos 4A.................(1)

sin 3A + 2sin 4A.................(2)

Put value of A in 1 and 2.

$\rule{200}{2}$

Taking (1)

cos 3(15)° - 2cos 4(15)°

⟹ cos 45° - 2 cos 60°

Put value of cos 45° and cos 60°.

$\sf{⟹ \: \frac{1}{ \sqrt{2} } - 2( \frac{1}{2}) } \\ \\ \sf{⟹ \frac{1}{ \sqrt{2} } - \frac{ \cancel2}{\cancel2}} \\ \\ \sf{⟹ \frac{1}{ \sqrt{2} } - 1 } \\ \\ \sf{⟹ \frac{1 - \sqrt{2} }{ \sqrt{2} } }$

$\rule{200}{2}$

Taking (2)

sin 3(15)° + 2sin 4(15)°

sin 45° + 2sin 60°

Put values of sin 45° and sin 60°.

$\sf⟹\frac{1}{ \sqrt{2} } - 2( \frac{ \sqrt{3} }{2}) \\ \\ \sf⟹ \frac{1}{ \sqrt{2} } - \frac{ \cancel2 \sqrt{ 3} }{ \cancel2} \\ \\ \sf⟹ \frac{1}{ \sqrt{2} } - \sqrt{3} \\ \\ \sf⟹ \frac{1 - \sqrt{6} }{ \sqrt{2} }$