What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?
A) sin 2θ B) cos 2θ C) tan 4θ D) cot 2θ
Answers
Answered by
0
Step-by-step explanation:
Gtan(5θ)+tan(3θ)
tan(5θ)−tan(3θ)
=
sin(5θ)
cos(5θ)
+
sin(3θ)
cos(3θ)
sin(5θ)
cos(5θ)
−
sin(3θ)
cos(3θ)
=
sin(5θ)cos(3θ)+cos(5θ)sin(3θ)
cos(5θ)cos(3θ)
sin(5θ)cos(3θ)−cos(5θ)sin(3θ)
cos(5θ)cos(3θ)
=
sin(5θ)cos(3θ)+cos(5θ)sin(3θ)
sin(5θ)cos(3θ)−cos(5θ)sin(3θ)
=
sin(5θ+3θ)
sin(5θ−3θ)
⎡
⎣
⎢
⎢
⎢
Since,sin(A±B)
=sin(A)cos(B)±cos(A)sin(B)
⎤
⎦
⎥
⎥
⎥
=
sin(8θ)
sin(2θ)
=
2sin(4θ)cos(4θ)
sin(2θ)
⎡
⎣
⎢
⎢
⎢
Since,sin(2A)
=2sin(A)cos(A)
⎤
⎦
⎥
⎥
⎥
=
2(2sin(2θ)cos(2θ))cos(4θ)
sin(2θ)
⎡
⎣
⎢
⎢
⎢
Since,sin(2A)
=2sin(A)cos(A)
⎤
⎦
⎥
⎥
⎥
=
4sin(2θ)cos(2θ)cos(4θ)
sin(2θ)
=4cos(2θ)cos(4θ)
Similar questions