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# If Tan Theta = 1/Sqrt2 Find the Value of (Cosec^2 Theta - Sec^2 Theta)/(Cosec^2 Theta + Cot^2 Theta) - Mathematics

#### Question

if tan theta = 1/sqrt2 find the value of (cosec^2 theta - sec^2 theta)/(cosec^2 theta + cot^2 theta)

#### Solution

Given tan theta = 1/sqrt2

We have to find the value of the expression (cosec^2 theta - sec^2 theta)/(cosec^2 theta + cot^2 theta)

We know that,

1 +cot^2 theta = cosec^2 theta

=> cosec^2 theta - cot^2 theta = 1

Therefore, the given expression can be written as

(cosec^2 theta - sec^2 theta)/(cosec^2 theta + cot^2 theta) = (cosec^2 theta - sec^2 theta)/(1 + cot^2 theta + cot^2 theta)

tan theta = 1/sqrt2 => cot theta = sqrt2

(cosec^2 theta - sec^2 theta)/(1 + 2 cot^2 theta) = (1 + cot^2 theta -  (1 + tan^2 theta))/(1 + 2 cot62 theta)             (since sec^2 theta    =1 + tan^2 theta)

= (cot^2 theta - tan^2 theta)/(1 + 2 cot^ theta)

= ((sqrt2)^2 - (1/sqrt2)^2)/(1 + 2 xx (sqrt2)^2)

= 3/10

Hence, the value of the given expression is 3/10

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 11: Trigonometric Identities
11.2 | Q: 3 | Page no. 54
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 11: Trigonometric Identities
11.2 | Q: 3 | Page no. 54
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If Tan Theta = 1/Sqrt2 Find the Value of (Cosec^2 Theta - Sec^2 Theta)/(Cosec^2 Theta + Cot^2 Theta) Concept: Trigonometric Ratios of Complementary Angles.
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