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

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### 3 Answers

E = sin90*cos60 - sin30 + tg45*ctg135

= 1 (1/2) - (1/2) + tg45 * ctg135

= 1/2 -1/2 + 1* ctg135

= ctg135

= ctg(135) = tg(90-135) = tg(-45) = -tg45= -1

==> E = -1

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**

To calculate E = sin90cos60-sin30 + tgt45*ctg135

Solution:

sin90 = 1.

cos 60 = 1/2

tangent 45 =1

ctgt135 = -tgt 45 = -1.

Therefore substituting in the exptression,

E = 1*(1/2)-(1/2) + 1*(-1) = -1