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CBSE Class 10 Answered

if sinθ +cosθ =1,prove that cosθ -sinθ =±1
Asked by Gounshi | 23 Nov, 2018, 04:43: PM
answered-by-expert Expert Answer
sin θ + cos θ = 1
 
(sin θ + cos θ)2 = sin2 θ + cos2 θ - 2sin θ cos θ = 1.................(1)
 
since sin2 θ + cos2 θ =1, from eqn.(1), we have sin θ cos θ = 0 ................(2)
 
( cos θ - sin θ )2 = cos2θ + sin2θ  - 2 cosθ sinθ = 1 - 0 = 1
 
cos θ - sin θ = ±1
 
Answered by Thiyagarajan K | 23 Nov, 2018, 09:31: PM
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