10th Math Sample Paper 2019 | Q17 Choice 1

This 2019 CBSE class 10 Maths 3 mark question is from Trigonometry. An easy 3 mark question testing concepts in rewriting tan θ and cot θ in term of sin θ and cos θ and basic trigonometric identities.

Question 17A: Prove that cot θ – tan θ = \\frac{2 cos^2 θ – 1}{sin θ cos θ})

Video Explanation

Explanatory Answer | CBSE Sample Paper 2019 Question 17 Choice 1

LHS : cot θ – tan θ
= \\frac{cos θ}{sin θ}) - \\frac{sin θ}{cos θ})
= \\frac{cos^2 θ – sin^2 θ}{sin θ cos θ})

We know sin² θ + cos ² θ = 1
Rewrite sin²θ in the numerator as (1 - cos²θ): \\frac{cos^2 θ − (1− cos^2 θ)}{sin θ cos θ}) = \\frac{cos^2 θ − 1 + cos^2 θ}{sin θ cos θ})
= \\frac{2 cos^2 θ – 1}{sin θ cos θ})