Question

sec^2 65 - cot^2 25 -2sin30 cos60

Answer 1

Answer:

See the pic below

Answer 2

Concept:

We need to know few trigonometric equtions like the below:

If Cot x= Cot(90-y), then Cot x=Tan y

$sec^{2}x- tan^{2}x=1$

$Sin30=\frac{1}{2} \ and\ cos60= \frac{1}{2}$

Given:

The following trigonometric equation is given:

$sec^{2}65-cot^{2} 25-2sin30cos30$

To find:

We need to find the value of the given equation.

Solution:

Now, we know that

25°=90°-65°

Then

$cot25=cot(90-65)$

⇒$cot25=tan65$

Therefore

$sec^{2}65-tan^{2} 65-2sin30cos30$

⇒$1-2(\frac{1}{2})(\frac{1}{2} )$             [$sec^{2}x- tan^{2}x=1$]

⇒$1-\frac{1}{2}$

⇒$\frac{1}{2}$

Therefore the value  of the trigonometric equation is $\frac{1}{2}$