Question #04552

1 Answer
May 12, 2017

Use sin(theta)=cos(90^@-theta). Answer: 2

Explanation:

Evaluate (sin39^@/cos51^@)^2+(cos51^@/sin39^@)^2

Here, it is important to note that sin(theta)=cos(90^@-theta) and cos(theta)=sin(90^@-theta)

Therefore, by substitution:

(sin39^@/cos51^@)^2+(cos51^@/sin39^@)^2

=(cos(90^@-39^@)/cos51^@)^2+(cos51^@/cos(90^@-39^@))^2

=(cos51^@/cos51^@)^2+(cos51^@/cos51^@)^2

=1^2+1^2

=2

Therefore, our answer is 2.