Question

Question no.7 of this image

Plzzz... urgent

Answer 1

Step-by-step explanation:

1-cosec^2 A (tan^2A)

=cot^2×tan^2A

=1

Answer 2

Answer:

We can calculate the value of given by breaking into sin and cos trigonometric ratios.

Following properties will be used:-)

$tan^2 A = \frac{{sin}^{2}A}{{cos}^{2}A}\\\\cosec^2 A=\frac{1}{{sin}^{2}A}\\\\1-{sin}^{2}A={cos}^{2}A$

Value of

$(1 - {cosec}^{2} A) {tan}^{2} A$

can be calculated as follows

$(1 - {cosec}^{2} A) {tan}^{2} A \\ \\ = (1 - \frac{1}{ {sin}^{2} A} ) \frac{ {sin}^{2}A }{ {cos}^{2} A} \\ \\ = \frac{ {sin}^{2} A}{ {cos}^{2} A} - \frac{1}{ {cos}^{2} A} \\ \\ = \frac{ {sin}^{2} A- 1}{ {cos}^{2} A} \\ \\ \frac{ - (1 - {sin}^{2} A)}{ {cos}^{2}A } \\ \\ = \frac{ - {cos}^{2} A}{ {cos}^{2} A} \\ \\ = - 1$

OR

As we know that

$cosec^2 A -1 = cot ^2 A \\ and \\ cot^2 A \times tan^2 A =1$

$(1 - {cosec}^{2} A) {tan}^{2} A \\ \\ = -cot^2 A \times tan^2 A \\ \\ = -1$