# What is the relation between sec and tan, cosec and cot, sin and cos?

How to prove that $sin^2 \theta + cos^2 \theta =1$?

L.H.S = $sin^2 \theta + cos^2 \theta = (\frac{AB}{AC})^2 + (\frac{BC}{AC})^2=\frac{AB^2+BC^2}{AC^2}$   (1)

But, we have $AB^2 + BC^2 = AC^2$ according to Pythagoras Theorem.

Putting this in (1), we get

L.H.S= $\frac{AC^2}{AC^2}=1=R.H.S$

Therefore, we have $sin^2 \theta + cos^2 \theta = 1$

Similarly, we can prove that $sec^2 \theta - tan^2 \theta = 1$

And, $cosec^2 \theta - cot^2 \theta = 1$

Posted in : NCERT Solutions, Trigonometry

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