Question

in the given figure ab is equal to 3 cm BC is equal to 4 cm find the value of cosec square theta minus cot square theta​

Answer 1

Step-by-step solution:

Given:

AB = 3 cm

BC = 4 cm

To find:

Value of cosec^2 theta - cot^2 theta

Solution:

tan theta = AB/BC

= 3/4

hence, cot^2 theta = (4/3)^2

= 16/9

Now, we apply Pythagorean theorem to this triangle and we get AC to be 5 cm.

hence, cosec theta = AC/AB

= 5/3

cosec^2 theta = (5/3)^2

= 25/9

Now,

the value of cosec^2 theta - cot^2 theta:

= 16/9 - 25/9

= 16 - 25/9

= -9/9

= -1

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