Question

IfA= cos0+ sin'e, than prove that for all values of o, 12 / SASI.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

If cos θ – sin θ = √2 sin θ, then cos θ + sin θ is equal to

1) √2 cos θ

2) √2 sin θ

3) 2 cos θ

4) -√2 cos θ

Answer: (1) √2 cos θ

Solution:

Given,

cos θ – sin θ = √2 sin θ

Squaring on both sides,

cos2θ + sin2θ – 2 sin θ cos θ = 2 sin2θ

1 – 2 sin θ cos θ = 2 sin2θ

2 sin θ cos θ = 1 – 2 sin2θ….(i)

Now,

cos θ + sin θ

Squaring this expression,

(cos θ + sin θ)2 = cos2θ + sin2θ + 2 sin θ cos θ

= 1 + 1 – 2 sin2θ {from (i)}

= 2 – 2 sin2θ

= 2(1 – sin2θ)

= 2 cos2θ

Therefore, cos θ + sin θ = √2 cos θ