Question

sec^6theta+cos^6theta=1-3sin^2thetacos^2theta​

Answer 1

Answer:

good question

Step-by-step explanation:

Given:- 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.