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
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Question 7
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
CBSE Class 10 Sample Paper for 2018 Boards
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