Question

if 12sin theta = 35 cos theta, find sin theta - cos theta/sin theta + cos theta

Answer 1

Answer:

pls use like this formula

Step-by-step explanation:

sinθ+cosθ=

2

cosθ

To prove:- cosθ+sinθ=

2

sinθ

Proof:-

sinθ+cosθ=

2

cosθ

Squaring both sides, we get

sin

2

θ+cos

2

θ+2sinθcosθ=2cos

2

θ

⇒sin

2

θ−cos

2

θ+2sinθcosθ=0

Subtracting 2sin

2

θ both sides, we have

−sin

2

θ−cos

2

θ+2sinθcosθ=−2sin

2

θ

sin

2

θ+cos

2

θ−2sinθcosθ=2sin

2

θ

(cosθ−sinθ)

2

=2sin

2

θ

⇒cosθ−sinθ=

2

sinθ

Hence proved.