Find x from the following equations : cosec π 2 + θ + x cos θ cot π 2 + θ = sin π 2 + θ

We have cosec π 2 + θ + x cos θ cot π 2 + θ = sin π 2 + θ ⇒ sec θ + x cos θ [ - tan θ ] = cos θ ⇒ sec θ - x cos θ tan θ = cos θ ⇒ 1 cos θ - x cos θ × sin θ cos θ = cos θ ⇒ 1 - cos 2 θ cos θ = x sin θ ⇒ sin 2 θ cos θ sin θ = x ⇒ sin θ cos θ = x ⇒ tan θ = x ∴ x = tan θ

Find x from the following equations : x cot π 2 + θ + tan π 2 + θ sin θ + cosec π 2 + θ = 0

We have: x cot 90 ° + θ + tan 90 ° + θ sin θ + cosec 90 ° + θ = 0 ⇒ x [ - tan θ ] + [ - cot θ ] sin θ + sec θ = 0 ⇒ - x tan θ - cot θ sin θ + sec θ = 0 ⇒ - x × sin θ cos θ - cos θ sin θ × sin θ + 1 cos θ = 0 ⇒ - x sin θ - cos 2 θ + 1 cos θ = 0 ⇒ - x sin θ - cos 2 θ + 1 = 0 ⇒ - x sin θ + sin 2 θ = 0 ⇒ x = sin θ .

Prove that tan 5 π 4 cot 9 π 4 + tan 17 π 4 cot 15 π 4 = 0

Given that, LHS = tan 225 ° cot 405 ° + tan 765 ° cot 675 ° = tan π + π 4 cot 2 π + π 4 + tan 4 π + π 4 cot 4 π + π 4 = tan π 4 cot π 4 + tan π 4 - cot π 4 = tan π 4 cot π 4 - tan π 4 tan π 4 = 1 × 1 - 1 × 1 = 0 = RHS Hence proved

E M B I B E

MATHEMATICS for CLASS XI>Chapter 5 - Trigonometric Functions>EXERCISE 5.3

R D Sharma Solutions for Chapter: Trigonometric Functions, Exercise 3: EXERCISE 5.3

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Trigonometric Functions, Exercise 3: EXERCISE 5.3

Attempt the practice questions on Chapter 5: Trigonometric Functions, Exercise 3: EXERCISE 5.3 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.