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What is the Value of (1 + Tan2 θ) (1 − Sin θ) (1 + Sin θ)? - Mathematics

Sum

What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?

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Solution

We have, 

`(1+tan^2θ)(1-sinθ)(1+sin θ)=(1+tan ^2 θ){(1-sinθ)(1+sinθ)}` 

                            = `(1+tan^2θ)(1-sin^2θ)` 

We know that, 

`sec^2θ-tan^2θ=1` 

⇒ `sec^2 θ=1+tan^2θ` 

`sin^2 θ+cos ^2θ=1` 

⇒ `cos^2 θ=1sin^2θ` 

Therefore, 

`(1+tan^2θ)(1-sin θ)(1+sin θ)  = sec^2 θ xxcos^2θ`

                                          = `1/cos^2θ xx cos^2 θ` 

                                         =` 1`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Q 15 | Page 55
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