Question

if theta is equal to 45 then prove sin 2 theta is equal to 2 cos theta into cos 3 theta

Answer 1

Solution :

Here I am using A instead of theta.

A = 45° ( given )

LHS = sin2A

= sin( 2× 45° )

= sin90°

= 0 ----( 1 )

RHS = 2cosAcos3A

= 2cos 45° cos 3( 45° )

= 2cos45cos135°

= 2co45° cos( 90 + 45° )

= 2cos45°[ -sin 45° ]

= - 2sin45cos45


= - sin ( 2×45 )

= - sin90°

= 0

Therefore ,

LHS = RHS

If A = 45° then

sin2A = 2cosAcos3A

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