Question

Pls solve all these . I need it urgently. wrong answer will be reported so who know only they answer
the 1st one who answered right will be the brainlist answer



pls answer it fast I need it urgently ​

Answer 1

Answer:

I am taking theta as x

5 )

Sin ^ 2 x + Sin ^ 2 x * tan ^2 x

= Sin ^ 2 x ( 1 + tan ^2 x )

= Sin ^ 2 x (sec ^2 x )

= tan ^2 x

HENCE PROVED

6 )

tan ^2 x - sin^2 x

= sin^2 x /cos^2 x - sin ^2 x

= sin ^2 x ( 1/cos^2x - 1 )

= sin^2 x ( sec^2 x -1 )

= sin^2 x ( tan ^2 x )

HENCE PROVED

7)

cos ^2 x ( 1 + tan ^2 x ) + sin^2 x ( 1 + cot ^2 x )

= cos ^2 x + cos ^2 x * tan ^2 x + sin^2 x + sin^2 x * cot ^2 x

= cos ^2 x + sin^2 x + sin^2 x + cos ^2 x

= 1 + 1

= 2

HENCE PROVED

11)

(sec x - 1 )/(sec x + 1 )

= { ( 1/ cos x ) -1 } / { ( 1/cos x) + 1 }

=( 1 - cos x ) / (1 + cos x)

multiplying 1 + cos x on numerator and denominator

= 1 - cos ^2 x / (1 + cos x)^2

= sin ^ 2 x / (1 + cos x)^2

={ sin x / ( 1 + cos x ) } ^ 2

HENCE PROVED

12 )

(1 / sin x ) / { ( cos x / sin x) + tan x }

= (1 / sin x ) / { ( cos x / sin x) + (sin x / cos x) }

= (1 / sin x ) / {( cos ^2 x + sin ^2 x ) / sin x cos x }

= { (1 / sin x ) (sin x cos x ) } /1

= cos x

HENCE PROVED

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Answer 2

Answer:

refer to the attachment for the solution.

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