Question

tan theta is equal to 3 upon 4 then prove that cosec 2 theta - sec 2 theta upon cosec 2 theta + sec 2 theta.

Answer 1

Proper Question :

tan θ = ¾

To Prove : Cosec²θ - Sec²θ / Cosec²θ + Sec²θ


Given : tan θ = ¾

✒ tan θ = p/b = ¾

h² = p² + b²

h² = (3)² + (4)²

h ² = 25

h = 5 unit

Now, Cosec θ = 5/3

✏ Sec = 5/4


Now, Substitute these value in Given Equation!

Cosec²θ - Sec²θ / Cosec²θ + Sec²θ

✏ (5/3)² - ( 5/4)² / (5/3)² + (5/4)²

✏ 25/9 - 25/16 ÷ 25/9 + 25/16

✏ 400 - 225/144 ÷ 400 + 225/144

✏ 175/144 ÷ 625/144

✏ 175/625


✏ 35/125

✏ 7/25



Hence, Required Value of Cosec²θ - Sec²θ / Cosec²θ + Sec²θ is 7/25.

Answer 2

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QUESTION :)

✔✔✔tan theta is equal to 3 upon 4 then prove that cosec 2 theta - sec 2 theta upon cosec 2 theta + sec 2 theta.

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ANSWERS :)✔✔✔

Ans.

After evaluating given sum

The answer comes 1/2

This is shown in the picture below

tan theta=3/4

or,cot theta=1/tan theta=1/3/4=4/3

or,cot^2theta=16/9

Now, sin theta=(1/cosec^2 theta)^1/2

=[1/(1+cot^2 theta)]^1/2

So,sin theta=[1/(1+16/9)]^1/2

=[1/(16+9)/9]^1/2

=(9/25)^1/2

or,sin theta=3/5

Again, sec theta=1/cos theta

or,sec theta=[1/(1-sin^2 theta)]^1/2

or,sec theta=[1/(1-9/25)]^1/2

or, sec theta=[25/(25-9)]^1/2

or, sec theta=(25/16)^1/2

or, sec theta=5/4

Ans: sin theta=3/5 & sec theta=7/25

answer =7/25