The value of \( \Large \left(\frac{1}{(1+tan^{2} \theta )}+\frac{1}{(1+cot^{2} \theta )}\right) \) is


A) 1

B) 2

C) \( \Large \frac{1}{2} \)

D) \( \Large \frac{1}{4} \)

Correct Answer:
A) 1

Description for Correct answer:
\( \Large \frac{1}{1+tan^{2} \theta }+\frac{1}{1+cot^{2} \theta } \)

\( \Large \frac{1}{1+\frac{sin^{2} \theta }{cos^{2} \theta }}+\frac{1}{1+\frac{cos^{2} \theta }{sin^{2} \theta }} \)

= \( \Large \frac{cos^{2} \theta }{cos^{2} \theta +sin^{2} \theta }+\frac{sin^{2} \theta }{sin^{2} \theta +cos^{2} \theta } \)

\( \Large cos^{2} \theta +sin^{2} \theta =1 \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry








Comments

No comments available




Similar Questions
1). The minimum value of \( \Large sin^{2} \theta+cos^{4} \theta \) is
A). \( \Large \frac{1}{\sqrt{2}} \)
B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{3}{4} \)
D). \( \Large \frac{2}{3} \)
-- View Answer
2). If \( \Large sec \theta +tan \theta =2 \), what is the value of \( \Large sec \theta \) ?
A). \( \Large \frac{3}{2} \)
B). \( \Large \sqrt{2} \)
C). \( \Large \frac{5}{2} \)
D). \( \Large \frac{5}{4} \)
-- View Answer
3). What is \( \Large sin 25^{\circ} sin 35^{\circ}  sec 65^{\circ} sec 55^{\circ}\) equal to?
A). -1
B). 0
C). \( \Large \frac{1}{2} \)
D). 1
-- View Answer
4). If p = a sin x + b cos x and q = a cos x - b sin x, then what is the of \( \Large p ^{2}+q^{2} \) ?
A). a + b
B). ab
C). \( \Large a ^{2}+b^{2} \)
D). \( \Large a ^{2}-b^{2} \)
-- View Answer
5). What is the value of \( \Large sec(90 ^{\circ} - \theta) \ sin \theta sec45^{\circ}\)?
A). 1
B). \( \Large \frac{\sqrt{3}}{2} \)
C). \( \Large \sqrt{2} \)
D). \( \Large \sqrt{3} \)
-- View Answer


6). If \( \Large tan \theta =\frac{4}{3} \) then the value of \( \Large \frac{3 \ sin \theta +2 \ cos \theta }{3 \ sin \theta -2 \ cos \theta } \) is
A). 0.5
B). -0.5
C). 3
D). -3
-- View Answer
7). If \( \Large sec \theta -cosec \theta =0 \), then the value of \( \Large tan \theta +cot \theta \) is
A). 0
B). 1
C). -1
D). 2
-- View Answer
8). If \( \Large tan \ 7 \theta \ tan \ 2 \theta=1 \),then the value of \( \Large tan \ 3 \theta \) is
A). \( \Large \sqrt{3} \)
B). \( \Large -\frac{1}{\sqrt{3}} \)
C). \( \Large \frac{1}{\sqrt{3}} \)
D). \( \Large -\sqrt{3} \)
-- View Answer
9). The expression \( \Large \frac{tan 57 ^{\circ} +cot 37 ^{\circ} }{tan 33 ^{\circ} + cot 53 ^{\circ} } \) is equal to
A). tan 33 \(^{\circ}\) cot 57\(^{\circ}\)
B). tan 57 \(^{\circ}\)cot 37 \(^{\circ}\)
C). tan 33 \(^{\circ}\)cot 53 \(^{\circ}\)
D). tan 53 \(^{\circ}\) cot 37 \(^{\circ}\)
-- View Answer
10). The numerical value of \( \Large \frac{5}{sec^{2} \theta }+\frac{2}{1+cot^{2} \theta }+3 \ sin^{2} \theta \) is
A). 5
B). 2
C). 3
D). 4
-- View Answer