If x = a sin t and y = b tan t , prove that a 2 x 2 - b 2 y 2 = 1

To Prove : a 2 x 2 - b 2 y 2 = 1 Given that, x = a sin t and y = b tan t ⇒ sin t = x a and tan t = y b ⇒ cosec t = a x and cot t = b y We know that, cosec 2 t - cot 2 t = 1 ⇒ a 2 x 2 - b 2 y 2 = 1 Hence, proved.

If m = cos α cos β and n = cos α sin β , show that m 2 + n 2 cos 2 β = n 2 .

Given that, m = cos α cos β and n = cos α sin β To prove : m 2 + n 2 cos 2 β = n 2 ⇒ cos α cos β 2 + cos α sin β 2 cos 2 β = n 2 ⇒ cos 2 α sin 2 β + cos 2 α cos 2 B cos 2 β sin 2 β cos 2 β = n 2 ⇒ cos 2 α sin 2 β + cos 2 β sin 2 β = n 2 ⇒ cos 2 α sin 2 β = n 2 ⇒ cos α sin β 2 = n 2 ⇒ n 2 = n 2 Hence, proved.

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Understanding ISC Mathematics Class 11 Volume 1>Chapter 3 - Trigonometry>EXERCISE 3.2

M L Aggarwal Solutions for Chapter: Trigonometry, Exercise 2: EXERCISE 3.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Trigonometry, Exercise 2: EXERCISE 3.2

Attempt the practice questions on Chapter 3: Trigonometry, Exercise 2: EXERCISE 3.2 with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 1 solutions are prepared by Experienced Embibe Experts.