if sin a-cos a=1/2then find the value of 1/sin a+cos a.
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Answer:
Step-by-step explanation:
SinA - CosA = 1/2
//Squaring on both sides
(SinA - CosA)² = 1/4
Sin²A + Cos²A - 2SinACosA = 1/4
2SinACosA = 1 - 1/4 = 3/4
(SinA + CosA)² = Sin²A + Cos²+ 2SinACosA
= 1 + 3/4 = 7/4
=> SinA + CosA = √(7/4) = √7/2
=> 1/SinA + CosA = 1/(√7/2) = 2/√7 = 2/√7 * √7/√7 = 2√7/7.
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