Question

(tan A x sin A)+ cos A = sec A

Answer 1

Answer:

$\Large{\underline{\underline{\bf{Given:}}}}$

• (tan A × sin A) + cos A = sec A

$\Large{\underline{\underline{\bf{To\:Prove:}}}}$

LHS = RHS

$\Large{\underline{\underline{\bf{Proof:}}}}$

→ Taking the LHS of the equation,

$(\dfrac{sin\:A}{cos\:A} \times sin\:A)+cos\:A$

$=(\dfrac{sin^{2}\:A }{cos\:A} )+cos\:A$

→ Cross multiplying

$=\dfrac{sin^{2}\:A+cos^{2}\:A }{cos\:A}$

$=\dfrac{1}{cos\:A}$

$=sec\:A$

= RHS

Hence proved.

$\Large{\underline{\underline{\bf{Identities\:used:}}}}$

→ $tan\:A=\dfrac{sin\:A}{cos\:A}$

→$sin^{2}\:A+cos^{2}\:A=1$

→$\dfrac{1}{cos\:A} =sec\:A$