Question

Prove that :
$sin {}^{2}theta + \frac{1}{1 + \tan {}^{2} theta } = 1$
​

Answer 1

Step-by-step explanation:

Maths

Prove that:

tanθ−secθ+1

secθ+tanθ−1

=

1−sinθ

cosθ

Put 1=sec

2

θ−tan

2

θ=(secθ−tanθ)(secθ+tanθ)

⟹

tanθ−secθ+1

secθ+tanθ−(secθ−tanθ)(secθ+tanθ)

⟹

(1−secθ+tanθ)

secθ+tanθ(1−secθ+tanθ)

⟹secθ+tanθ

Put secθ=

cosθ

1

and tanθ=

cosθ

sinθ

⟹

cosθ

1

+

cosθ

sinθ

Multiply and divide by 1−sinθ

⟹

cosθ(1−sinθ)

1−sin

2

θ

⟹

1−sinθ

cosθ

Answer 2

Answer:

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