2A is measure of acute angle and sec 2 A =operatorname{cosec}( A -42), then value of A is ldots ldot

English

Gujarati

Hindi

8. Introduction to Trigonometry

medium

$2A$ is the measure of acute angle and $\sec 2 A =\operatorname{cosec}( A -42),$ then the value of $A$ is $\ldots \ldots \ldots \ldots$

A

$44$

B

$43$

C

$44.5$

D

$42.5$

Solution

$\sec 2 A =\operatorname{cosec}( A -42)$

$\therefore \operatorname{cosec}(90-2 A )=\operatorname{cosec}( A -42)$

$\therefore 90-2 A = A -42$

$\therefore 90+42=3 A$

$\therefore 3 A =132$

$\therefore A =44$

Standard 10

Mathematics

Share

Similar Questions

For acute angles $A$ and $B,$ if $\tan A=1$ and $\sin B=\frac{1}{\sqrt{2}},$ then $\cos (A+B)=\ldots \ldots \ldots$

easy

Prove that,

$(\sqrt{3}+ 1) \left(3-\cot 30^{\circ}\right)=\tan ^{3} 60^{\circ}-2 \sin 60^{\circ}$

medium

Prove that $\sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos ^{2} \theta=1$

medium

$\cos \theta=\frac{15}{17},$ then the value of $\operatorname{cosec} \theta+\cot \theta $ is ………

easy

$\sin 60 \sin 45+\cos 60 \cos 45=\ldots \ldots \ldots \ldots$

easy