Question

3. If cas o -bsino =c, prove Asino+ bcoso
= +-√ a²+ b 2 - c2​

Answer 1

Answer:

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If acosθ+bsinθ=m and asinθ−bcosθ=n, then the value of a

2

+b

2

is

Medium

Solution

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Correct option is D)

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

Step-by-step explanation:

search-icon-header

Search for questions & chapters

search-icon-image

Question

Bookmark

If acosθ+bsinθ=m and asinθ−bcosθ=n, then the value of a

2

+b

2

is

Medium

Solution

verified

Verified by Toppr

Correct option is D)

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