Question

tan²A+cot²A=sec²A cosec²A-2

plz solve this​

Answer 1

Step-by-step explanation:

tan²A + cot²A + 2 = sec²A × cosec²A

tan²A + cot²A = sec²A × cosec²A - 2

LHS = tan²A + cot²A

= (sec²A - 1 ) + (cosec²A - 1)

= sec²A + cosec²A - 2

\begin{gathered}=\frac{1}{{cos}^{2}\alpha} + \frac{1}{{sin}^{2}\alpha} - 2 \\ \\ = \frac{{cos}^{2}\alpha + {sin}^{2}\alpha}{{cos}^{2}\alpha× {sin}^{2}\alpha}- 2 \\ \\ \huge\boxed{{sin}^{2}\theta + {cos}^{2}\theta = 1} \\ \\ = \frac{1}{{cos}^{2}\alpha\: {cosec}^{2}\alpha} -2\\ \\= {sec}^{2}\alpha \:{cosec}^{2}\alpha - 2 \\ \\\end{gathered}

=

cos

2

α

1

+

sin

2

α

1

−2

=

cos

2

α×sin

2

α

cos

2

α+sin

2

α

−2

sin

2

θ+cos

2

θ=1

=

cos

2

αcosec

2

α

1

−2

=sec

2

αcosec

2

α−2

HENCE PROVED