Question

Value of sec Square 26 degrees - cot square 64 degrees is

Please answer in a little bit detail ​

Answer 1

The result is 1

Explanation:

we have

`sec^(2)(26\°)-cot^2(64\°)`

Remember that

`cot^2(64\°)=(cos^2(64\°))/(sin^2(64\°))`

`sec^(2)(26\°)=(1)/(cos^2(26\°))`

If two angles are complementary ----> A+B=90°

then

cos (A)=sin(B)

In this problem 26° and 64° are complementary angles

therefore

`(1)/(cos^2(26\°))=(1)/(sin^2(64\°))`

substitute

`(1)/(sin^2(64\°))-(cos^2(64\°))/(sin^2(64\°))`

`(1-cos^2(64\°))/(sin^2(64\°))`

we have that

`1-cos^2(64\°)=sin^2(64\°)`

substitute

`(sin^2(64\°))/(sin^2(64\°))=1`