Question

1+ cot²A/1-cosec²A = sec²A(prove that)​

Answer 1

Answer:

sec²A = sec²A

Step-by-step explanation:

Hence proved

Answer 2

Answer:

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

Step-by-step explanation:

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