Math, asked by Nitya8, 1 year ago

If tanα=1/7, find the value of  \frac{ cosec^{2} \alpha - sec^{2} \alpha   }{ cosec^{2} \alpha + sec^{2} \alpha   }


Nitya8: please don't answer the question...i got it!!
rational: okay sounds great :)
Nitya8: :D
Nitya8: TeeHee......i changed the question!
Nitya8: Please answer this one!!!
Nitya8: this different from the one i posted before :)
rational: okay will try...
Nitya8: thankuuuuu :)

Answers

Answered by rational
2
\dfrac{\csc^2\alpha-\sec^2\alpha}{\csc^2\alpha+\sec^2\alpha}

Using reciprocal identities \csc\alpha = \frac{1}{\sin\alpha}, ~\sec\alpha=\frac{1}{\cos\alpha} the given expression becomes
\dfrac{\frac{1}{\sin^2\alpha}-\frac{1}{\cos^2\alpha}}{\frac{1}{\sin^2\alpha}+\frac{1}{\cos^2\alpha}}

Multiply top and bottom by \sin^2\alpha and get
\dfrac{1-\tan^2\alpha}{1+\tan^2\alpha}

Plugin the given value and simplify
\dfrac{1-\left(\frac{1}{7}\right)^2}{1+\left(\frac{1}{7}\right)^2}~=~\dfrac{49-1}{49+1}~=~\dfrac{48}{50}~=~\dfrac{24}{25}

Nitya8: thank u soooooo much!!!!
rational: np :)
rational: hey there is a mistake in last line, im gonna fix it
Nitya8: okie
rational: done!
Nitya8: hey i asked another question, can u try to do it plzz
Nitya8: :)
rational: i tried a bit and gave up as it got complicated lol il give it a try again..
Nitya8: ok np
Nitya8: ;)
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