Question

Class 10
Topic - Trigonometry
Prove that -

tanθ/(secθ - 1) + tanθ/(secθ + 1) = 2cosecθ

Answer 1

Answer:

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Answer 2

Solution :-

Some trigonometric identities used :

tanθ = secθ/cosecθ

sec²θ - 1 = tan²θ

Q: tanθ/(secθ - 1) + tanθ/(secθ + 1) = 2cosecθ

L.H.S : tanθ/(secθ - 1) + tanθ/(secθ + 1)

On rationalizing :

tanθ/(secθ - 1) × (secθ + 1)/(secθ + 1) + tanθ/(secθ + 1) × (secθ - 1)/(secθ - 1)

= tanθ(secθ + 1)/secθ² - 1 + tanθ(secθ - 1)/sec²θ - 1

= tanθ(secθ + 1)/tan²θ + tanθ(secθ - 1)/tan²θ

= (secθ + 1)/tanθ + (secθ - 1)tanθ

= secθ/tanθ + 1/tanθ + secθ/tanθ - 1/tanθ

= 2secθ/tanθ

= (2secθ × cosecθ)/secθ

= 2cosecθ = R.H.S

Hence, Proved