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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) \( \Large \sqrt{3} \)

Correct Answer:



C) \( \Large \sqrt{2} \)

Description for Correct answer:

Given, \( \Large sec(90- \theta ) ^{\circ} sin \theta sec 45 \)

= \( \Large cosec \theta sin \theta \ sec \ 45 ^{\circ} \)

= \( \Large \frac{1}{sin \theta }.sin \theta .(\sqrt{2})=\sqrt{2} \)

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

Comments

Similar Questions

1). 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

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2). If \( \Large sec \theta -cosec \theta =0 \), then the value of \( \Large tan \theta +cot \theta \) is

A). 0

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3). If \( \Large tan \ 7 \theta \ tan \ 2 \theta=1 \),then the value of \( \Large tan \ 3 \theta \) is

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4). The expression \( \Large \frac{tan 57 ^{\circ} +cot 37 ^{\circ} }{tan 33 ^{\circ} + cot 53 ^{\circ} } \) is equal to

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6). The value of tan 4\(^{\circ}\).tan 43\(^{\circ}\).tan 47 \(^{\circ}\).tan 86 \(^{\circ}\) is

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7). Consider the following equations

\( \Large cosec^{2}x+sec^{2}x=cosec^{2}x \ sec^{2}x \)

\( \Large sec \ x+tan^{2}x=sec \ x \ tan^{2}x \)

\( \Large cosec \ x+tan^{2}x=cot^{2}x+sec \ x \)

Which of the above equations are correct?

A). (i) and (ii)

B). (ii) and (iii)

C). (i) and (iii)

D). (i), (ii) and (iii)

8). If \( \Large \frac{cos \ x}{1+cosec \ x}+\frac{cosx}{cosec\ x-1}=2 \) ,which one of the following is one of the value of x ?

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

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

C). \( \Large \frac{ \pi }{4} \)

D). \( \Large \frac{ \pi }{6} \)

9). \( \Large \frac{cos \theta }{1-sin \theta }-\frac{cos \theta }{1+sin \theta }=2 \),is satisfied by which one of the following values of \( \Large \theta \)?

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

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

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D). \( \Large \frac{ \pi }{6} \)

10). What is \( \Large \sqrt{\frac{1+sin \theta }{1-sin \theta }} \) equal to?

A). \( \Large sec \theta -tan \theta \)

B). \( \Large sec \theta +tan \theta \)

C). \( \Large cosec \theta +cot \theta \)

D). \( \Large cosec \theta -cot \theta \)