Math Instructor

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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