Question

Prove that cosec squared 56 minus tan squared 34 is equal one

Answer 1

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given that cosec²56 - tan²34

to prove that it is equal to one

L.H.S :

we know cosec ( 90 - θ ) = secθ

where θ  = the angle formed

=> cosec²( 90 - θ  ) = sec²θ

=> cosec² ( 90 - 34 ) = sec²34

=> sec²34 - tan²34

{ 1 + tan²θ = sec²θ }

=> { sec²θ - tan²θ = 1 }

substitute θ with 34

=> sec²34 - tan²34 = 1

L.H.S = R.H.S

hence proved

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Answer 2

Step-by-step explanation:

cosec^2 56 - tan^2 34 = 1

sec(90 - angle) = cosec( angle )

so

sec^2 34 - tan ^2 34 = 1

we know that tan^2 theta + 1 = sec^2 theta

so

sec^2 theta - tan^2 theta = 1

so

sec^2 34 - tan^2 34 = 1

therefore

1 = 1

hence proved