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Prove the Following Identities, Where the Angles Involved Are Acute Angles for Which the Expressions Are Defined - CBSE Class 10 - Mathematics

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Question

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

 

Solution

L.H.S

`= (cosec θ – cot θ)^2`

`=(1/sintheta - costheta/sintheta)^2`

`=(1-costheta)^2/(sin theta)^2 = (1-cos theta)^2/(sin^2theta)`

`= (1-costheta)^2/(1-cos^2 theta) = (1-costheta)^2/((1-costheta)(1+cos theta)) = (1-cos theta)/(1+costheta)`

= R.H.S

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 8: Introduction to Trigonometry
Ex. 8.40 | Q: 5.01 | Page no. 193
Solution Prove the Following Identities, Where the Angles Involved Are Acute Angles for Which the Expressions Are Defined Concept: Trigonometric Identities.
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