Question

If tan = a/b find sin2 + cos2​

Answer 1

Answer:

Answer is

Step-by-step explanation:

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Question

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If tanθ=

b

a

then the value of bcos2θ+asin2θ is

Medium

Solution

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Correct option is B)

tanθ=

b

a

⇒1+tan

2

θ=sec

2

θ⇒1+(

b

a

)

2

=sec

2

θ⇒

b

2

a

2

+b

2

=sec

2

θ⇒cos

2

θ=

a

2

+b

2

b

2

⇒

cosθ=

a

2

+b

2

b

2

we know that, sinθ=

1−

a

2

+b

2

b

2

=

a

2

+b

2

a

2

Now, bcos2θ+asin2θ=b(cos

2

θ−sin

2

θ)+a(2sinθcosθ)=b(

a

2

+b

2

b

2

−

a

2

+b

2

a

2

)+a(2

a

2

+b

2

ab

)

=

b

2

+a

2

1

[b

3

−a

2

b+2a

2

b]=

b

2

+a

2

b

3

+a

2

b

=

b

2

+a

2

b(b

2

+a

2

)

=b