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Questions
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following:
`tan theta + 1/tan theta` = sec θ.cosec θ
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Solution
We know that `sec^2 theta - tan^2 theta = 1`
So,
`tan theta + 1/tan theta = (tan^2 theta + 1)/tan theta`
`= sec^2 theta/tan theta`
`= sec theta sec theta/tan theta`
`= sec theta = (1/cos theta)/(sin theta/cos theta)`
`= sec theta cosec theta`
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If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ...[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
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If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
