Question

If x=3 sec square theta -1 , y=tan square theta-2 the find value of x-3y

Answer 1

hey mate it's ur answer

Answer 2

Answer:

8 is the required answer of x- 3y

Step-by-step explanation:

Explanation:

Given , x = 3$sec^2\theta$ - 1  and y = $tan^2\theta$ - 2

Let x - 3y  ........(i)      [∴ Given ]

Put the  the given value of x and y in equation (i)

Step 1:

On putting x = 3$sec^2\theta$ - 1 and y =  $tan^2\theta$ - 2 in (i) we get ,

x - 3y = (3$sec^2\theta$ - 1 ) - 3 (  $tan^2\theta$ - 2)

⇒3$sec^2\theta$ - 1 - 3  $tan^2\theta$ + 6

⇒3$sec^2\theta$ - 3$tan^2\theta$ + 5

Now take  3 as common from $sec^\theta\ and\ tan^ 2\theta$ ,

⇒ 3 ($sec^2\theta$ - $tan^2\theta$ ) + 5

⇒3 $(\frac{1}{cos^2\theta } - \frac{sin^2\theta }{cos^2\theta } )$ + 5

⇒3( $\frac{1 - sin^2\theta}{cos^2\theta}$ )+ 5   ⇒ 3 ×$\frac{cos^2\theta }{cos^2 \theta }$ + 5         [∴ $1- sin^2\theta = cos^2\theta$]

⇒ 3 × 1 + 5 = 8      [where $cos^2\theta \ and \ cos^2\theta$ are cancel out ]

Final answer:

Hence , value of (x- 3y ) is 8 .

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