Prove that , sinA /secA + 1 + sinA /secA -1 = 2cotA
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Answer:
Step-by-step explanation:
sinA /secA + 1 + sinA /secA -1
= SinA(SecA - 1) + SinA(SecA + 1)/ (SecA - 1)(SecA + 1)
= SinASecA - SinA + SinASecA + SinA / Sec²A - 1
= 2SinASecA/ Tan²A (∵ Sec²A - Tan²A = 1)
= 2SinASecA/Sin²A/Cos²A
= 2SinA*Cos²A / Sin²A . CosA (∵ SecA = 1/CosA)
= 2 CosA/SinA
= 2 CotA
= R.H.S
Hence proved
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