Question

if x = 3 sec squared theta minus 1, Y equal 10 squared theta minus 2 then find the value of x - 3y

Answer 1

Answer:

The value of expression is $x-3y=8$      

Step-by-step explanation:

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

To find : The value of $x-3y$

Solution :

Write the expression  $x-3y$

Substitute, the values of x and y given

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

Solving,

$x-3y =3\sec^2\theta-1-3\tan^2\theta+6$

$x-3y=3(sec^2\theta-\tan^2\theta)+5$

Applying trigonometric identity,

$sec^2\theta-\tan^2\theta=1$

We get,

$x-3y=3(sec^2\theta-\tan^2\theta)+5$

$x-3y=3(1)+5$

$x-3y=8$

Therefore, The value of expression is $x-3y=8$

Answer 2

Answer:

$Value \:of \:x-3y = 8$

Step-by-step explanation:

$Given\:x=3sec^{2}\theta -1\:---(1)\\y=tan^{2}\theta-2\:---(2)$

$Value \:of \: x-3y\\=(3sec^{2}\theta-1) -3(tan^{2}\theta-2)\\=3sec^{2}\theta-1 -3tan^{2}\theta+6\\=3sec^{2}\theta -3tan^{2}\theta+5\\=3(sec^{2}\theta-tan^{2}\theta)+5\\=3\times 1+5$

/* By Trigonometric identity:

Sec²A-tan²A=1 */

$=3+5\\=8$

Therefore,

$Value \:of \:x-3y = 8$

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