If sin π + cos π =√3, then prove that tan π + cot π = 1
CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
Question 32 (OR 1st question) If sin π + cos π =β3, then prove that tan π + cot π = 1 sin π + cos π =β3 Squaring both sides (sin π + cos π)2 = (β3)^2 (sin π + cos π)2 = 3 sin2 π + cos2 π + 2 cos ΞΈ sin ΞΈ = 3 Putting sin2 π + cos2 π = 1 1 + 2 cos ΞΈ sin ΞΈ = 3 2 cos ΞΈ sin ΞΈ = 3 β 1 2 cos ΞΈ sin ΞΈ = 2 cos ΞΈ sin ΞΈ = 1 We have to prove tan π + cot π = 1 Solving LHS tan π + cot π = sinβ‘π/cosβ‘π +cosβ‘π/sinβ‘π = (sin^2β‘π + cos^2β‘π)/(cosβ‘π sinβ‘π ) Putting sin2 π + cos2 π = 1 = 1/(cosβ‘π sinβ‘π ) From (1): cos ΞΈ sin ΞΈ = 1 = 1/1 = 1 = RHS Since LHS = RHS Hecne proved