If $cosec 39^{0}$ = x, the value of $\frac{1}{cosec^{2}51^{0}}+sin^{2}39^{0}+tan^{2}51^{0}-\frac{1}{sin^{2}51^{0}sec^{2}39^{0}}$ is
If $cosec 39^{0}$ = x, the value of $\frac{1}{cosec^{2}51^{0}}+sin^{2}39^{0}+tan^{2}51^{0}-\frac{1}{sin^{2}51^{0}sec^{2}39^{0}}$ is
1). $\sqrt{x^{2} - 1}$
2). $\sqrt{1 - x^{2}}$
3). $x^{2} - 1$
4). $1 - x^{2}$
2 answers
.$\frac{1}{cosec ^{2}51}+\sin^{2}39+\tan^{2}51 - \frac{1}{\sin^{2}51.sec^{2}39}$
= sin (90° – $\theta$) = cos $\theta$
tan (90° – $\theta$) = cot $\theta$]
= 1 + $\cot^{2}$39° – 1
= $cosec^{2}$ 39° – 1 = $x^{2}$ – 1
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