Calculate the expression: E=sin90*cos60-sin30+tg45*ctg135

Starting from the formula of complementary angle, we'll have:

sin a = cos (90-a)

cos a = sin (90-a)

tg a = ctg (90-a)

ctg a = tg (90-a)

Since the angles of 30 and 60 are complementary, we could write:

sin 30 = cos (90-30) = cos 60

ctg 135 = tg (90-135) = tg (-45) = -tg 45

We'll substitute the results into expression and we'll get:

E=sin90*cos60-cos60-tg45*tg45

We'll factorize and we'll get:

E=cos60(sin90-1) - (tg45)^2

We know that sin90=1 and tg45=1

Substituting the numerical values, we'll have:

E=cos60(1-1) - (1)^2

E=-1