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Q.

$cosec 69^{\circ} + \cot 69^{\circ}$ When expressed in terms of angles between $0^{0}$ and $45^{0}$ becomes.

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a

\sec 21^{\circ} + \tan 21^{\circ}

b

\sin 21^{\circ} + \cot 21^{\circ}

c

\sin 21^{\circ} + \cos 21^{\circ}

d

\sec 21^{\circ} + \cot 21^{\circ}

answer is A.

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Detailed Solution

Given expression is,

cosec 69^{\circ} + \cot 69^{\circ}

….. (1)
It is known that,

\cos A = \sin (90^{\circ} - A)

\cot A = \tan (90^{\circ} - A)

cosec A = \sec (90^{\circ} - A)

Using these values in equation (1) we get

cosec 69^{\circ} = cosec (90^{\circ} - 21^{\circ}) = \sec 21^{\circ}

\cot 69^{\circ} = \cot (90^{\circ} - 21^{\circ}) = \tan 21^{\circ}

Put the values in equation (1,)

cosec 69^{\circ} + \cot 69^{\circ} = \sec 21^{\circ} + \tan 21^{\circ}

So, the correct option is 1.

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