Question

IF AN ANGLE TAN THETA =1/ROOT7 FIND THE VALUE OF COSEC² THETA –SEC² THETA /COSEC² THETA +SEC ² THETA

Answer 1

Answer:

GIVEN

TAN Θ =1/√7

TAN Θ=AB/AC

AB=1K

BC= √7 K

COT C Θ = AC/AB = 2√2

COSEC² Θ –SEC² Θ / COT² Θ +SEC ² Θ

( √7) ²

( AC)² =(AB)²+( BC)²

=(1K)²+(√7K)²

1K²+7K²

8K²

=2√2

GIVEN =TAN Θ = 1/

TAN Θ = AB/AC

AB=1K

BC = √7 K

COSEC Θ =AC/AB =2√2

SEC Θ =AC/BC =2√2 / 7

COSEC² Θ –SEC² Θ / COT² Θ +SEC ² Θ

4(2)_4(2)/7

=8+8/7

4(2)+ 4(2)/7

= 3/4

Answer 2

Given :-

$\huge\sf tan\theta = \dfrac{1}{\sqrt{7} }$

To find :-

$\dfrac{\sf cosec^{2} \theta - sec^{2} \theta}{\sf cosec^{2} + sec^{2} } = \ ?$

Solution :-

$\huge\sf tan\theta = \dfrac{1}{\sqrt{7} }$

Therefore , Tan theta = opposite side/adjacent side

tan theta=1/root 7

Therefore,

Opposite side=1 and Adjacent side= root 7

By Pythogoras theorem

Hypotenuse^2=Adjacent^2+Opposite^2

Hypotenuse^2 = root 7^2 + 1^2

Hypotenuse^2 = 7+1

Hypotenuse = root 8

Sin theta = Opposite/ Hypotenuse

Sin theta = 1/root 8

Therefore,

cosec theta = root 8/1

cos theta = Adjacent/Hypotenuse

Cos theta = root 7/root 8

Therfore,

sec theta = root 8/ root 7

Now ,

Cosec^2 theta - Sec^2 theta / Cosec^2 theta + Sec^2 theta

Root 8^2/1^2 - Root8^2/root 7^2 / root 8^2/1^2 + root8^2/root 7^2

8/1-8/7 / 8/1+8/7

56-8/7 /56+8/7

48/7 / 64/7

48/7 *7/64

 48/64

= 3/4

The answer is 3/4