Question

Prove that sec/sin- sin/cos=cot​

Answer 1

$\purple{\huge{\bold{\mathcal{Answer}}}}$

$\frac{ \sec }{ \sin } - \frac{sin}{cos} \\ \frac{sec \times cos - sin {}^{2} }{sin \times cos} \\ \frac{ \frac{1}{cos} \times cos - sin {}^{2} }{sin \times cos} \\ \frac{1 - sin {}^{2} }{sin \times cos} \\ \frac{cos {}^{2} }{sin \times cos}$

$\purple{\huge{\bold{\boxed{\mathcal{cos/sin=cot}}}}}$

Answer 2

Answer:

HAYE MATE HER YOUR ANSWER

(sinA - cosA)(cotA + tanA)=secA - cosecA

lhs → (sinA - cosA)[(cosA/sinA) + (sinA/cosA)]

=(sinA - cosA)(cos²A + sin²A/sinAcosA)

=(sinA - cosA)(1)/sinAcosA

=(sinA - cosA)/sinAcosA

=1/cosA - 1/sinA

=secA - cosecA

rhs → secA - cosecA

lhs=rhs

hence proved

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