Question

(sin thetha +cos thetha )^2=1+2 sin thetha cos thetha
​

Answer 1

Step-by-step explanation:

Consider the given equation.

sinθ+2cosθ=1 ……… (1)

On squaring both sides, we get

(sinθ+2cosθ)

2

=1

2

sin

2

θ+4cos

2

θ+4sinθcosθ=1

We know that

sin

2

θ=1−cos

2

θ

cos

2

θ=1−sin

2

θ

Therefore,

1−cos

2

θ+4(1−sin

2

θ)+4sinθcosθ=1

−cos

2

θ+4−4sin

2

θ+4sinθcosθ=0

−cos

2

θ−4sin

2

θ+4sinθcosθ=−4

4sin

2

θ+cos

2

θ−4sinθcosθ=4

(2sinθ−cosθ)

2

=4

2sinθ−cosθ=2

Hence, proved

Answer 2

If it’s not clear you can ask !