Question

1 + 10 square theta (1 - sin square theta is equals to 1
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Answer 1

Let's prove

`\boxed{\sf 1+tan^2\theta(1-sin^2\theta)=1}`

LHS

`\\ \sf\longmapsto 1+tan^2\theta(1-sin^2\theta)`

`\\ \sf\longmapsto 1+(sin^2\theta)/(cos^2\theta)(1-sin^2\theta)`

`\\ \sf\longmapsto (cos^2\theta+sin^2\theta)/(cos^2\theta)(1-sin^2\theta)`

`\\ \sf\longmapsto (1)/(cos^2\theta)(1-sin^2\theta)`

`\\ \sf\longmapsto (1-sin^2\theta)/(cos^2\theta)`

`\\ \sf\longmapsto (1-sin^2\theta)/(1-sin^2\theta)`

`\\ \sf\longmapsto 1`

Hence provee