Question

prove that sinA×secA+cosA×cosecA=secA×cosecA​

Answer 1

Question :-

Prove that :

$\red{\sin a \: \times \sec a} \: + \cos a \: \green{ \times \cosec a \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sec a \: \times \cosec a \:$

Proof :-

Taking LHS

$\to \: \red{\sin a \: \times \sec a} \: \green{ + \cos a \:{ \times \cosec a \:} } \: \\ \\ \sf \because \: \sec a = \frac{1}{ \cos a} \: \: and \: \: \cosec a = \frac{1}{ \sin a} \\ \\ \to \: \frac{ \sin a}{ \cos a} + \green{ \frac{ \cos a}{ \sin a}} \\ \\ \to \frac{ \red{{ \sin}^{2}a + { \cos}^{2}a }}{ \purple{\cos a \: \sin a}} \\ \\ \because \boxed{ { \sin}^{2} \theta + { \cos}^{2} \theta = 1} \\ \\ \to \pink{ \: \frac{1}{ \cos a} }\times \frac{1}{ \sin a} \\ \\ \to \sec a \: \cosec a \:$

Hence proved ; )

Answer 2

Answer:

Step-by-step explanation:

= sinA * 1/cosA + cosA * 1/sinA

=sinA/cosA + cosA/sinA

= (sin^{2}A+cos^{2}A)/cosAsinA

=1/cosAsinA

=1/cosA * 1/sinA

=secA * cosecA

=RHS