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inna [77]
3 years ago
7

Prove the identity (cot x sin x)(sec x – cos x) = sin^2x

Mathematics
2 answers:
hram777 [196]3 years ago
8 0

Answer:

[(cosx/sinx)(sinx)][(1/cosx) - cosx]

(cosx)[(1 - cos²x)/cosx]

1 - cos²x

sin²x

FrozenT [24]3 years ago
7 0

Step-by-step explanation:

(cot x \: sinx)(secx - cosx) =  {sin}^{2} x \\  \\ lhs = (cot x \: sinx)(secx - cosx)  \\  =  (cot x \: sinx) \times secx \\- (cot x \: sinx) \times cosx \\  \\  =  \frac{cosx}{sinx}  \times sinx \times secx\\ -  \frac{cosx}{sinx}  \times sinx \times cosx \\  = cosx \times secx - cosx \times cosx \\ =  1 -  {cos}^{2} x \\  =  {sin}^{2} x \\ =  rhs \\ hence \: proved

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