If A = cos 2 θ + sin 4 θ , then prove that for all values of θ , 3 4 ≤ A ≤ 1 .

Given: A = cos 2 θ + sin 4 θ To prove: 3 4 ≤ A ≤ 1 , for all values of θ A = cos 2 θ + sin 2 θ sin 2 θ ⇒ A = cos 2 θ + sin 2 θ 1 - cos 2 θ ⇒ A = cos 2 θ + sin 2 θ - sin 2 θ cos 2 θ ⇒ A = 1 - sin 2 θ cos 2 θ ∵ sin 2 θ + cos 2 θ = 1 ⇒ A = 1 - sin 2 θ cos 2 θ ≤ 1 . . . 1 Again, A = cos 2 θ + sin 4 θ ⇒ A = 1 - sin 2 θ + sin 4 θ ⇒ A = sin θ - 1 2 2 + 3 4 ⇒ A ≥ 3 4 . . . 2 From equation 1 and 2 , we get 3 4 ≤ A ≤ 1 Hence, proved.

E M B I B E

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)

Odisha Board Solutions for Chapter: Trigonometric Functions, Exercise 1: Exercises- 4(a)

Author:Odisha Board

Odisha Board Mathematics Solutions for Exercise - Odisha Board Solutions for Chapter: Trigonometric Functions, Exercise 1: Exercises- 4(a)

Attempt the free practice questions on Chapter 4: Trigonometric Functions, Exercise 1: Exercises- 4(a) with hints and solutions to strengthen your understanding. Bureau's Higher Secondary Elements of Mathematics Vol.1 solutions are prepared by Experienced Embibe Experts.

Questions from Odisha Board Solutions for Chapter: Trigonometric Functions, Exercise 1: Exercises- 4(a) with Hints & Solutions

EASY

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 3

Find the domains of tangent and cotangent functions.

EASY

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 4

Determine the ranges of sine and cosine functions.

EASY

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 5

Find a value of $A$ when $\cos 2 A = \sin 3 A$ .

EASY

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 6

Find the value of $\cos 1 ° . \cos 2 ° \dots . . \cos 100 °$ .

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 7

Find the value of $\cos 24 ° + \cos 5 ° + \cos 175 ° + \cos 204 ° + \cos 300 °$ .

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 8

Evaluate $\tan \frac{π}{20} . \tan \frac{3 π}{20} . \tan \frac{5 π}{20} . \tan \frac{7 π}{20} . \tan \frac{9 π}{20}$ .

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 4 - Trigonometric Functions>Exercises- 4(a)>Q 9

Show that $\frac{\sin^{3} (180 ° + A) . \tan (360 ° - A) . \sec^{2} (180 ° - A)}{\cos^{2} (90 ° + A) {cosec}^{2} A . \sin (180 ° - A)} = \tan^{3} A$ .