**Proving Trigonometric Identities Worksheet with Solutions :**

Here we are going to see some practice questions on proving trigonometric identities. For each question you may find solution in a single click.

(1) Determine whether each of the following is an identity or not.

(i) cos²θ + sec²θ = 2 + sin θ

(ii) cot²θ + cos θ = sin² θ

(2) Prove the following identities

(i) sec²θ + cosec²θ = sec²θ cosec²θ Solution

(ii) sin θ /(1 - cos θ) = cosec θ + cot θ Solution

(iii) √ (1 - sin θ)/(1 + sin θ) = sec θ - tan θ Solution

(iv) cos θ/(sec θ - tan θ) = 1 + sin θ Solution

(v) √( sec²θ + cosec²θ) = tan θ + cot θ Solution

(vi) (1 + cos θ - sin²θ)/(sin θ)(1 + cosθ) = cot θ

(vii) sec θ (1 - sin θ)(sec θ + tan θ) = 1 Solution

(viii) sin θ/(cosec θ + cot θ) = 1 - cos θ Solution

(3) Prove the following identities

(i) [sin (90 - θ)/(1 + sin θ)] + [cos θ/(1 - (cos (90 - θ))] = 2 sec θ Solution

(ii) tan θ/(1 - cot θ) + cot θ/(1 - tanθ) = 1 + secθ cosecθ

(iii) sin (90 - θ)/(1 - tan θ) + cos (90 - θ)/(1 - cot θ) = cosθ + sin θ Solution

(iv) [tan (90 - θ)/(cosec θ + 1)] + [(cosec θ + 1)/cot θ)] = 2 sec θ Solution

(v) (cot θ + cosec θ - 1)/(cot θ - cosec θ + 1) = cosec θ + cotθ Solution

(vi) (1 + cotθ - cosecθ) (1 + tanθ + secθ) = 2 Solution

(vii) (sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ-tanθ)

(viii) tan θ/(1-tan²θ)= sin θ sin (90 - θ)/[2 sin²(90-θ) - 1]

(ix) [1/(cosec θ - cot θ)] - (1/sin θ) = [(1/sinθ)]-[1/(cosec θ + cot θ)] Solution

(x) (cot²θ + sec²θ)/(tan²θ + cosec²θ)

= sinθ cosθ (tanθ + cotθ) Solution

(4) If x = a sec θ + b tan θ and y = a tan θ + b sec θ then prove that x² - y² = a² - b² Solution

After having gone through the stuff given above, we hope that the students would have understood, how to prove trigonometric identities worksheet with solutions.

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