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CBSE Class 11-science Answered

class 11

Asked by kushik.jnp2025 | 15 Jan, 2023, 12:00: AM

Expert Answer

begin mathsize 14px style L e t space space f space equals space square root of fraction numerator 1 plus sin x over denominator 1 minus sin x end fraction end root space equals space square root of u over v end root end style

begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space 1 half square root of fraction numerator 1 minus sin x over denominator 1 plus sin x end fraction end root space fraction numerator d over denominator d x end fraction open parentheses u over v close parentheses end style

begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space 1 half square root of fraction numerator 1 minus sin x over denominator 1 plus sin x end fraction end root space space open parentheses fraction numerator v space begin display style fraction numerator d u over denominator d x end fraction end style space minus space u space begin display style fraction numerator d v over denominator d x end fraction end style over denominator v squared end fraction close parentheses end style

........................... (1)

begin mathsize 14px style fraction numerator d u over denominator d x end fraction space equals space fraction numerator d over denominator d x end fraction left parenthesis 1 plus sin x right parenthesis space equals space cos x end style

begin mathsize 14px style fraction numerator d v over denominator d x end fraction space equals space fraction numerator d over denominator d x end fraction left parenthesis 1 minus sin x right parenthesis space equals space minus cos x end style

By substituting u, v, du/dx and dv/dx in eqn.(1) , we get

begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space 1 half square root of fraction numerator 1 minus sin x over denominator 1 plus sin x end fraction end root space space open parentheses fraction numerator left parenthesis 1 minus sin x right parenthesis cos x space plus space left parenthesis 1 plus sin x right parenthesis cos x over denominator left parenthesis 1 minus sin x right parenthesis squared end fraction close parentheses end style

begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space 1 half square root of fraction numerator 1 over denominator 1 plus sin x end fraction end root space space open parentheses fraction numerator 2 over denominator left parenthesis 1 minus sin x right parenthesis square root of 1 minus sin x end root end fraction close parentheses space equals space square root of fraction numerator 1 over denominator 1 minus sin squared x end fraction end root space open parentheses fraction numerator 1 over denominator 1 minus sin x end fraction close parentheses end style

begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space fraction numerator 1 over denominator cos x space left parenthesis 1 minus sin x right parenthesis end fraction end style

Answered by Thiyagarajan K | 15 Jan, 2023, 11:12: AM

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