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The value of the expression \( \Large 1 - \frac{\sin^{2} y}{1+\cos y}+\frac{1 + \cos y}{\sin y}-\frac{\sin y}{1- \cos y} \) is equal to;

A) 0
B) 1
C) \( \Large \sin y \)
D) \( \Large \cos y \)

Correct Answer:




D) \( \Large \cos y \)

Description for Correct answer:
The given expression can be written as

\( \Large \frac{1+\cos y - \sin^{2}y}{1+\cos y} + \frac{ \left(1-\cos^{2}y\right)-\sin^{2}y }{\sin y \left(1-\cos y\right) } \)

= \( \Large \frac{\cos y \left(1+\cos y\right) }{1+\cos y}+0= \cos y \)

Part of solved Trigonometric ratio questions and answers : >> Elementary Mathematics >> Trigonometric ratio

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Similar Questions

1). The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1m. The angle subtended by the write at the centre of the circle is equal to:

A). \( \Large \frac{ \pi }{4}rad \)

B). \( \Large \frac{ \pi }{3}rad \)

C). \( \Large \frac{ \pi }{5}rad \)

D). \( \Large \frac{ \pi }{10}rad \)

2). The greatest and least value of \( \Large \sin x \cos\ x \) are:

A). 1, -1

B). \( \Large \frac{1}{2},\ -\frac{1}{2} \)

C). \( \Large \frac{1}{4},\ -\frac{1}{4} \)

D). 2, -2

3). If \( \Large A = \sin^{2} \theta + \cos^{4} \theta \), then for all real values of \( \Large \theta \)

A). \( \Large 1 \le A \le 2 \)

B). \( \Large \frac{3}{4} \le A \le 1 \)

C). \( \Large \frac{13}{16} \le A \le 1 \)

D). \( \Large \frac{3}{4} \le A \le \frac{13}{16} \)

4). \( \Large \tan \frac{2 \pi }{5} - \tan \frac{ \pi }{15} - \sqrt{3} \tan \frac{2 \pi }{5} \tan \frac{ \pi }{15} \) is equal to:

A). \( \Large -\sqrt{3} \)

B). \( \Large \frac{1}{\sqrt{3}} \)

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5). If \( \Large A = 130 ^{\circ} and\ x=\sin A + \cos A \), then:

A). \( \Large x > 0 \)

B). \( \Large x < 0 \)

C). \( \Large x=0 \)

D). \( \Large x \le 0 \)

6). If \( \Large A+B+C= \pi \ and\ \cos A = B \cos C,\ then\ \tan B \tan C \) is equal to:

A). \( \Large \frac{1}{2} \)

B). 2

C). 1

D). \( \Large -\frac{1}{2} \)

7). The period of \( \Large \sin^{2} \theta \) is

A). \( \Large \pi ^{2} \)

B). \( \Large \pi \)

C). \( \Large 2 \pi \)

D). \( \Large \frac{ \pi }{2} \)

8). If \( \Large y = \sin^{2} \theta + cosec^{2} \theta \), \( \Large \theta \ne 0 \), then

A). \( \Large y = 0 \)

B). \( \Large y \le 2 \)

C). \( \Large y \ge -2 \)

D). \( \Large y > 2 \)

9). If \( \alpha \) is a root of \( \Large 25 \cos^{2} \theta + 5 \cos \theta - 12 = 0,\) \( \Large \frac{\pi}{2} < \alpha < \pi \), then \( \Large sin 2\alpha \) is equal to

A). \( \Large \frac{24}{25} \)

B). \( \Large -\frac{24}{25} \)

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10). The value of \( \Large \cos \frac{ \pi }{65} \cos \frac{2 \pi }{65} \cos \frac{4 \pi }{65}.....\cos \frac{32 \pi }{65} \) is

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B). \( \Large \frac{1}{64} \)

C). \( \Large -\frac{1}{32} \)

D). \( \Large -\frac{1}{64} \)