ProofHard3 marks
Prove that √(sec² θ + cosec² θ) = tan θ + cot θ
Topic: Trigonometric identities
Previous-year question practice database
Answer
Solution diagram
Exam answer
Left-hand side = √(sec²θ + cosec²θ)
= √[(1+tan²θ)+(1+cot²θ)] = √(tan²θ+cot²θ+2).
Since tanθ·cotθ=1: tan²θ+cot²θ+2 = (tanθ+cotθ)².
Therefore: Left-hand side = tanθ+cotθ = Right-hand side.
Hence proved.
Explanation
Use sec²θ=1+tan²θ, cosec²θ=1+cot²θ and tanθcotθ=1.
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