Question

If x = 3 Sec2θ – 1 and y = 3tan2θ-2 then find the value of x – y

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Answer 1

SOLUTION

GIVEN

x = 3 sec²θ - 1 and y = 3tan²θ - 2

TO DETERMINE

The value of x - y

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

sec²θ - tan²θ = 1

EVALUATION

Here it is given that

x = 3 sec²θ - 1 and y = 3tan²θ - 2

Now

x - y

= ( 3 sec²θ - 1 ) - ( 3tan²θ - 2 )

= ( 3 sec²θ - 1 - 3tan²θ + 2 )

= ( 3 sec²θ - 3tan²θ + 1 )

= 3 ( sec²θ - tan²θ ) + 1

= ( 3 × 1 ) + 1

= 3 + 1

= 4

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