Question

10 points
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will mark as brainliest
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please help.

Answer 1

Hey Mate !

Here is your solution :

Note : I am not able to type the sign that has used, so I'm using α.

Given,

p = sin α + cos α

q = sec α + cosec α

Now,

R.H.S = 2p

Plug the value of p,

R.H.S = 2 ( sin α + cos α )

And,

L.H.S = q ( p² - 1 )

Substitute the value of q and p ,

= ( sec α + cosec α ) [ ( sin α + cos α )² - 1]

= ( sec α + cosec α ) ( sin² α + cos² α + 2 × sin α × cos α - 1 )

Using identity :

[ sin² α + cos² α = 1 ]

= ( sec α + cosec α ) ( 1 + 2 × sin α × cos α - 1 )

= ( sec α + cosec α ) ( 2 × sin α × cos α )

= 2 ( sec α + cosec α ) ( sin α × cos α )

Using identity :

=> sec α = 1 / cos α

=> cosec α = 1 / sin α

= 2 × [ ( 1/cos α ) + ( 1 / sin α ) ] ( sin α × cos α )

= 2 ( sin α × cos α ) [ ( sin α + cos α ) / ( sin α × cos α ]

=> 2 ( sin α + cos α ) = R.H.S

☆ Proved ☆

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Hope it helps !! ^_^