If \alpha + \beta = 90^\circ then the expression 1/3 is equal to :

RRB Junior Engineer Stage 1 Model Papers 1

Question : 18 of 100

Marks: +1, -0

α + β = 90°

then the expression

1/3

is equal to :

Solution:

α + β = 90°⇒β=90°-α

={\tan α}/{\tan β}+\sin^2α+\sin^2β

={\tan(90°-β)}/{\tanβ(90°-α)}+\sin^2(90-β)+\sin^2β

={\tanα}/{\cotα}+\cos^2β+\sin^2β=\tan^2α+1=\sec^2α

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