Math, asked by divya5448, 10 months ago

if tan theta equals to 1 upon root 5 what is the value of cosec squared theta minus sec squared theta upon cos squared theta + sec squared theta ​

Answers

Answered by MaheswariS
40

Answer:

\bf{\frac{cosec^2\theta-sec^2\theta}{cos^2\theta+sec^2\theta}=\frac{144}{61}}

Step-by-step explanation:

Given:

tan\theta=\frac{1}{\sqrt5}

\implies\:cot\theta=\sqrt5

sec^2\theta=1+tan^2\theta

sec^2\theta=1+\frac{1}{5}

sec^2\theta=\frac{6}{5}

\implies\:cos^2\theta=\frac{5}{6}

Now,

\frac{cosec^2\theta-sec^2\theta}{cos^2\theta+sec^2\theta}

=\frac{(1+cot^2\theta)-(1+tan^2\theta)}{cos^2\theta+sec^2\theta}

=\frac{cot^2\theta-tan^2\theta}{cos^2\theta+sec^2\theta}

=\frac{5-\frac{1}{5}}{\frac{5}{6}+\frac{6}{5}}

=\frac{\frac{25-1}{5}}{\frac{25+36}{30}}

=\frac{\frac{24}{5}}{\frac{61}{30}}

=\frac{24}{5}*\frac{30}{61}}

=\frac{24}{1}*\frac{6}{61}}

=\frac{144}{61}

Answered by TanikaWaddle
10

Given : \tan \theta = \frac{1}{\sqrt{5}}

To find : \frac{\csc^2\theta-\sec^2\theta}{\cos^2\theta+\sec^2\theta}

Step-by-step explanation:

\tan \theta = \frac{1}{\sqrt{5}}\\\\\cot \theta = \sqrt{5}\\\\\sec^2\theta= 1+ \tan^2\theta\\\\\sec^2\theta=1+\frac{1}{5}\\\\\sec^2\theta=\frac{6}{5}\\\\\cos^2\theta=\frac{5}{6}\\\\\frac{\csc^2\theta-\sec^2\theta}{\cos^2\theta+\sec^2\theta}\\\\\frac{(1-\cot^2\theta)-(1+\tan^2\theta)}{\cos^2\theta+\sec^2\theta}\\\\\frac{\cot^2\theta-\tan^2\theta}{\cos^2\theta+\sec^2\theta}\\\\\frac{5-\frac{1}{5}}{\frac{5}{6}+\frac{6}{5}}\\\\\frac{\frac{24}{5}}{\frac{61}{30}}\\\\\frac{24}{5}\times \frac{30}{61}

\\\\=\frac{144}{61}

#Learn more :

https://brainly.in/question/11433652

Similar questions