Question

tan 15 + cot 15 equal to 4

Answer 1

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Answer 2

The correct answer is 4.

Given: tan 15° + cot 15°.

To Prove: tan 15° + cot 15° = 4.

Solution:

tan 15° + cot 15°

=  $\frac{sin 15}{cos 15}+\frac{cos15}{sin15}$

=  $\frac{sin^{2}15 +cos^{2}15 }{sin15*cos15}$

Now, as we know

$sin^{2} x+cos^{2} x=1$

So, $sin^{2} 15+cos^{2} 15=1$

= $\frac{1}{sin15*cos15}$   (Multiply and divide by 2)

= $\frac{2}{2*sin15*cos15}$   (2*sin x*cos x = sin 2x)

=  $\frac{2}{sin 30}$

= $\frac{2}{\frac{1}{2} }$

= 4

Hence Proved.

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