Question

A+B=90, tan A=3/4, find cosec B

Answer 1

Step-by-step explanation:

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Answer 2

Given-A+B=90,

tan A=3/4

Find- cosec B

Solution-

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

$A+B=90^\circ$

$tanA=3/4$

$A=90^\circ-B$

$tan(90^\circ-B)=3/4$

$\Rightarrow cotB=3/4$

$1+cot^2B=cosec^2B$

$\Rightarrow 1+(3/4)^2=cosec^2B$

$\Rightarrow 1+9/16=cosec^2B$

$\Rightarrow 25/16=cosec^2B$

$\Rightarrow cosec B=\sqrt{25/16}$

$\Rightarrow cosecB=5/4$

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