Question

If sec^2 teta (1+sin teta) (1-sin teta) = k, find k

Pls help no spamming

Answer 1

Identities to be used :-

`\boxed{\sf 1-sin^2\theta=cos^2theta}`

`\boxed{\sf cos^2\theta=(1)/(sec^2\theta)}`

Solution:-

Let's do

`\\ \sf\longmapsto k=sec^2\theta(1+sin\theta)(1-sin\theta)`

`\\ \sf\longmapsto k=sec^2\theta(1-sin^2\theta)`

`\\ \sf\longmapsto k= sec^2\theta(cos^2\theta)`

`\\ \sf\longmapsto k=sec^2\theta* (1)/(sec^2\theta)`

`\\ \sf\longmapsto k=1`

Answer 2

`\color{lime}\boxed{\colorbox{black}{Answer : - }}`

`\sec^(2) θ(1 + \sinθ)(1 - \sinθ) = k`

`\sec^(2) θ \: (1 - { \sin}^(2) θ) = k`

`{ \sec }^(2) θ \cos^(2) θ = k`

`\sec ^(2) θ. \frac{1}{ {sec}^(2)θ } = k`

`1 = k`

Therefore:

`\color{red}k = 1`