If tan θ = a b , prove that a sin θ - b cos θ a sin θ + b cos θ = a 2 - b 2 a 2 + b 2 .

Given, tan θ = a b We need to prove a sin θ - b cos θ a sin θ + b cos θ = a 2 - b 2 a 2 + b 2 . Consider, LHS = a sin θ - b cos θ a sin θ + b cos θ Dividing numerator and denominator by cos θ , we get a sin θ cos θ - b cos θ cos θ a sin θ cos θ + b cos θ cos θ = a tan θ - b a tan θ + b = a × a b - b a × a b + b = a 2 - b 2 b a 2 + b 2 b = a 2 - b 2 a 2 + b 2 = RHS Hence, proved.

If 5 cos A - 12 sin A = 0 , then find the value of sin A + cos A 2 cos A - sin A .

Given, 5 cos A - 12 sin A = 0 . Now, cos A sin A = cot A = 12 5 . We know that, cot A = Adjacent Hypotenuse We need to find the value of sin A + cos A 2 cos A - sin A . By Pythagoras theorem, AC 2 = AB 2 + BC 2 ⇒ AC 2 = 12 2 + 5 2 ⇒ AC 2 = 169 ⇒ AC = 13 cm Now, sin A = Opposite Hypotenuse = BC AC = 5 13 cos A = Adjacent Hypotenuse = AB AC = 12 13 So, sin A + cos A 2 cos A - sin A = 5 13 + 12 13 2 × 12 13 - 5 13 = 17 13 24 - 5 13 = 17 13 19 13 = 17 19 Hence, the value of the given expression is 17 19 .

In a right angled △ ABC , if tan B = 12 5 , the find sin B .

Given, tan B = 12 5 . We know that, tan A = Opposite Adjacent We need to find the value of sin B . By Pythagoras theorem, AB 2 = AC 2 + CB 2 ⇒ AB 2 = 12 2 + 5 2 ⇒ AB 2 = 169 ⇒ AC = 13 cm Now, sin B = Opposite Hypotenuse = AC AB = 12 13 Hence, sin B = 12 13 .

If tan α = 5 12 , find the value of sec α .

Given, tan α = 5 12 . We know that, tan α = Opposite Adjacent We need to find the value of sec α . By Pythagoras theorem, AB 2 = AC 2 + CB 2 ⇒ AB 2 = 12 2 + 5 2 ⇒ AB 2 = 169 ⇒ AC = 13 cm Now, sec α = Hypotenuse Adjacent = AB AC = 13 12 Hence, sec α = 13 12 .

E M B I B E

CBSE Syllabus Standard Mathematics for Class X>Chapter 10 - Introduction to Trigonometry>Exercise 10.1

M L Aggarwal Solutions for Chapter: Introduction to Trigonometry, Exercise 1: Exercise 10.1

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Introduction to Trigonometry, Exercise 1: Exercise 10.1

Attempt the practice questions on Chapter 10: Introduction to Trigonometry, Exercise 1: Exercise 10.1 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class X solutions are prepared by Experienced Embibe Experts.