Question

If cos theta = m .Find sin theta​

Answer 1

Answer

Correct option is

D

m

2

+n

2

Given : acosθ+bsinθ=m ---( 1 )

asinθ−bcosθ=n ---( 2 )

Squaring (1) and (2), we get

a

2

cos

2

θ+b

2

sin

2

θ+2absinθcosθ=m

2

---(3)

and

a

2

sin

2

θ+b

2

cos

2

θ−2absinθcosθ=n

2

---(4)

Adding (3) and (4)

a

2

(sin

2

θ+cos

2

θ)+b

2

(sin

2

θ+cos

2

θ)=m

2

+n

2

or

a

2

+b

2

=m

2

+n

2

Answer 2

Answer:

sinθ = √1 - m²

Step-by-step explanation:

cosθ = m

squaring on both sides,

cos²θ = m²

by identity sin²θ + cos²θ = 1,

sin²θ + m² = 1,

∴ sin²θ = 1 - m²

sinθ = √1 - m²                         [sin theta = root(1 - m²)]

Hope that helps

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