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Question

How do you simplify cotx+tanx?


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Solution

Simplify using trigonometric laws:

The expression cotx+tanx can be simplified using trigonometric laws as follows,

cotx+tanx=cosxsinx+sinxcosx [tanθ=sinθcosθ,cotθ=cosθsinθ]

cotx+tanx=cosx2+sinx2sinx·cosx

cotx+tanx=cos2x+sin2xsinx·cosx

cotx+tanx=1sinx·cosx [sin2θ+cos2θ=1]

cotx+tanx=1sinx·cosx×22

cotx+tanx=22sinx·cosx

cotx+tanx=2sin2x [2sinθcosθ=sin2θ]

cotx+tanx=2cosec2x [1sinθ=cosecθ]

Hence, the simplest form of cotx+tanx obtained using trigonometric laws is 2cosec2x.


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