### Prove that cosβ‘ θ - sinβ‘θ + 1 /cosβ‘ θ + sinβ‘θ - 1 = cosec θ + cot θ

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here https://www.teachoo.com/cbse/sample-papers/

Last updated at Sept. 14, 2018 by Teachoo

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here https://www.teachoo.com/cbse/sample-papers/

Transcript

Question 27 Prove that cosβ‘γπ β sinβ‘π + 1γ/cosβ‘γπ + sinβ‘π β 1γ = cosec π + cot π Solving RHS cosec π + cot π Converting into cos and sin = 1/(sin π)+ cosβ‘π/sinβ‘π = (1 + cosβ‘π)/sinβ‘π Solving LHS cosβ‘γπ β sinβ‘π + 1γ/cosβ‘γπ + sinβ‘π β 1γ = cosβ‘γπ β sinβ‘π + 1γ/((cosβ‘γπ + sinβ‘π) β 1γ ) Question 27 Prove that cosβ‘γπ β sinβ‘π + 1γ/cosβ‘γπ + sinβ‘π β 1γ = cosec π + cot π Solving RHS cosec π + cot π Converting into cos and sin = 1/(sin π)+ cosβ‘π/sinβ‘π = (1 + cosβ‘π)/sinβ‘π Solving LHS cosβ‘γπ β sinβ‘π + 1γ/cosβ‘γπ + sinβ‘π β 1γ = cosβ‘γπ β sinβ‘π + 1γ/((cosβ‘γπ + sinβ‘π) β 1γ ) = γ(cosγβ‘γπ β sinβ‘π) + 1γ/((cosβ‘γπ + sinβ‘π) β 1γ ) Γ ((cosβ‘π+ sinβ‘π ) + 1)/((cosβ‘π+ sinβ‘π ) + 1) = (γ(cosγβ‘π + 1) β sinβ‘π)/((cosβ‘γπ + sinβ‘π) β 1γ ) Γ ((cosβ‘π + 1) + sinβ‘π)/((cosβ‘π+ sinβ‘π ) + 1) Using (a β b) (a + b) = a2 β b2 in numerator and denominator = (γγ(cosγβ‘π + 1)γ^2 β sin^2β‘π)/((cosβ‘π+ sinβ‘π )^2 β 1^2 ) = (cos^2β‘π + 1^2 + 2(1) cosβ‘π β sin^2β‘π)/(cos^2β‘π + sin^2β‘π + 2 cosβ‘π sinβ‘π β 1) = (cos^2β‘π +1 + 2 cosβ‘π β sin^2β‘π)/(cos^2β‘π + sin^2β‘π + 2 cosβ‘π sinβ‘π β 1) Using cos^2β‘π + sin^2β‘π = 1 in denominator = (cos^2β‘π +1 + 2 cosβ‘π β sin^2β‘π)/(1 + 2 cosβ‘π sinβ‘π β 1) = (cos^2β‘π + 1 + 2 cosβ‘π β sin^2β‘π)/(2 cosβ‘π sinβ‘π ) = (cos^2β‘π + 2 cosβ‘π + (1 β sin^2β‘π ))/(2 cosβ‘π sinβ‘π ) Using cos^2β‘π=1β sin^2β‘π in numerator = (cos^2β‘π + 2 cosβ‘π + cos^2β‘π)/(2 cosβ‘π sinβ‘π ) = (2 cos^2β‘π + 2 cosβ‘π )/(2 cosβ‘π sinβ‘π ) = (2 cosβ‘π (cosβ‘π + 1) )/(2 cosβ‘π sinβ‘π ) = (cosβ‘π + 1)/sinβ‘π = RHS β΄ LHS = RHS Hence proved

CBSE Class 10 Sample Paper for 2018 Boards

Paper Summary

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Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27 You are here

Question 28

Question 29

Question 30

Class 10

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.