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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
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Solution
y = tan θ (sin θ + cos θ)
`("d"y)/("d"x)` = tan θ (cos θ – sin θ) + (sin θ + cos 0) sec2 θ
= tan θ cos θ – tan θ sin θ + sin θ sec2θ + cos θ sec2θ
= `tan theta cos theta - tan theta sin theta + sintheta/(cos^2theta) + costheta/(cos^2theta)`
= `sin theta/cos theta cos theta - sin theta/cos theta sin theta + sin theta/cos theta * 1/cos theta + 1/costheta`
= sin θ – sin2θ sec θ + tan θ sec θ + sec θ
= sin θ + (1 – sin2θ) sec θ + sec θ tan θ
= `sin theta + cos^2theta xx 1/cos theta + sectheta tan theta`
= sin θ + cos θ + sec θ tan θ
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