((1+sinθ-cosθ)/(1+sinθ+cosθ))^2 is equal to (a) (1-cosθ)/(1+cosθ) (b) (1-sinθ)/(1+sinθ) (c) tan^

Name: Problem 36, Chapter 10: Comprehensive Mathematics for JEE Advanced
Uploaded: 2022-03-22T14:12:10-08:00
Duration: 4 min 37 s
Channel: Ankit Singh
Description: ((1+sinθ-cosθ)/(1+sinθ+cosθ))^2 is equal to (a) (1-cosθ)/(1+cosθ) (b) (1-sinθ)/(1+sinθ) (c) tan^2 (θ)/(2) (d) cot^2 (θ)/(2)

step 1 So we need to find which option is correct. So I'm just simplifying 1 plus sine theta minus pos

Question

$\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}$ is equal to (a) $\frac{1-\cos \theta}{1+\cos \theta}$ (b) $\frac{1-\sin \theta}{1+\sin \theta}$ (c) $\tan ^{2} \frac{\theta}{2}$ (d) $\cot ^{2} \frac{\theta}{2}$

   $\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}$ is equal to
(a) $\frac{1-\cos \theta}{1+\cos \theta}$
(b) $\frac{1-\sin \theta}{1+\sin \theta}$
(c) $\tan ^{2} \frac{\theta}{2}$
(d) $\cot ^{2} \frac{\theta}{2}$

Comprehensive Mathematics for JEE Advanced

Ravi Prakash; Ajay… 2019 Edition

Chapter 10, Problem 36

Instant Answer

Solved by Expert Ankit Singh

03/22/2022

Step 1

The numerator $1+\sin \theta-\cos \theta$ can be rewritten as $\sin^2 \frac{\theta}{2} + 2\cos^2 \frac{\theta}{2} - 2\sin \frac{\theta}{2}\cos \frac{\theta}{2} - \cos^2 \frac{\theta}{2} - \sin^2 \frac{\theta}{2}$. This simplifies to $(\cos \frac{\theta}{2} + Show more…

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$\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}$ is equal to (a) $\frac{1-\cos \theta}{1+\cos \theta}$ (b) $\frac{1-\sin \theta}{1+\sin \theta}$ (c) $\tan ^{2} \frac{\theta}{2}$ (d) $\cot ^{2} \frac{\theta}{2}$

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Key Concepts

Algebraic Manipulation in Trigonometry

Algebraic manipulation in trigonometry involves techniques such as factoring, expanding, and rationalizing expressions that contain trigonometric functions. These techniques are crucial for transforming complex expressions into simpler or more useful forms, often revealing underlying trigonometric relationships.

Trigonometric Identities

Trigonometric identities are equations involving trigonometric functions that are true for every value of the variable where both sides of the equality are defined. They form the basis for simplifying and transforming trigonometric expressions and are essential for solving equations in trigonometry.

Half-Angle Identities

Half-angle identities express trigonometric functions of an angle in terms of functions of half that angle. These identities are particularly useful for rewriting expressions to simplify problems and for integrating or differentiating trigonometric functions.

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