Questions & Answers

Question

Answers

A. 1

B. 2

C. 5

D. 0

Answer
Verified

In case of the trigonometric functions in Quadrant I all the functions are positive, in Quadrant II Sin and Cosec functions are positive and other functions are negative, in Quadrant III tan and cot functions are positive and other are negative and in the case of Quadrant IV Cos and Sec functions are positive and other being negative.

In this question for the given equation we will cofunction identities of the trigonometric function.

By the rule of cofunction identity,\[\sin \theta = \cos \left( {{{90}^ \circ } - \theta } \right)\]

We can write as:

\[

\sin \theta = \cos \left( {{{90}^ \circ } - \theta } \right) \\

\sin {15^ \circ } = \cos \left( {{{90}^ \circ } - {{15}^ \circ }} \right) \\

= \cos \left( {{{75}^ \circ }} \right) \\

\\

\]

We can also write, \[\cos \left( {{{75}^ \circ }} \right) = \cos \left( {5 \times {{15}^ \circ }} \right) = \cos \left( {n \times {{15}^ \circ }} \right)\]

Hence, the value of n=5,

Where \[\sin {15^ \circ }\]and \[\cos \left( {{{75}^ \circ }} \right)\]both lie in the Quadrant I where all the trigonometric functions are positive. Quadrant I lie in the range of \[0 - {90^ \circ }\].

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