Question

m answer right answer..... ​

Answer 1

Answer:

2cosec

Step-by-step explanation:

make use of cross multiplication:

(sinФ * sinФ + ( 1+cosФ)^2 ) / ( sinФ * ( 1 + cosФ))

= (sin^2 + ( 1+cosФ)^2 )

( 1+cosФ)^2 =

          ( 1 + cosФ) ( 1 + cosФ)

          1 + 2cosФ +cos^2Ф

 =  (sin^2 +  1 + 2cosФ +cos^2Ф ) / ( sinФ * ( 1 + cosФ))

make use of the trigonometry formula :

$sin^{2} + cos^{2} = 1$

= (1 + 1 + 2cosФ) /  ( sinФ * ( 1 + cosФ))

= ( 2+ 2cosФ) / ( sinФ * ( 1 + cosФ))

we can factorize the (2) in the numerator

=  (2 (1 + cosФ)) / ( sinФ * ( 1 + cosФ))

* cancel out the ( 1 + cosФ)

= 2 / sinФ

recall

sin inverse is equal to cosecant

hence answer is 2cosec

Answer 2

Step-by-step explanation:

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