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Step-by-step explanation:
it's cos x not cos ²x in denominator
now ,take LCM
and identity used: sin²a +cos²a = 1
see attachment for your answer
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Correct Question :-
Prove :- (1+sinA)/cosA + cosA/(1+sinA) = 2secA
Solution :-
Solving LHS,
→ (1+sinA)/cosA + cosA/(1+sinA)
Taking LCM,
→ [(1+sinA)² + cos²A] / cosA.(1+sinA)
using (a + b)² = a² + b² + 2ab in Numerator Now,
→ [1+sin²A+2sinA + cos²A] / cosA.(1+sinA)
Putting sin²A +cos²A = 1 in Numerator Now,
→ (1+1+2sinA)/cosA(1+sinA)
→ (2 + 2sinA) / cosA(1+sinA)
Taking 2 common From Numerator,
→ 2(1+sinA)/cosA(1+sinA)
cancel (1 + sinA) from N & D,
→ (2/cosA)
using (1/cosA) = secA now,
→ 2secA = RHS (Proved).
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