(Cos 70+cos20)÷ (sin70+sin20)

Answer 1

To simplify this expression, we first need to use the sum-to-product identities to convert the sums of sines and cosines into products:

cos(70) + cos(20) = 2 cos((70+20)/2) * cos((70-20)/2)
= 2 cos(45) * cos(25)
= sqrt(2) * cos(25)

sin(70) + sin(20) = 2 sin((70+20)/2) * cos((70-20)/2)
= 2 sin(45) * cos(25)
= sqrt(2) * sin(25)

Now, the expression becomes:

(sqrt(2) * cos(25)) / (sqrt(2) * sin(25))

Canceling out the square roots, we get:

cos(25) / sin(25)

Finally, applying the quotient identity for tan:

tan(25)