Question

1)) tg(270° + a). sinº(180° + a) + tg315°=2)) ctg^2(360°-a)0•cos^2(270°+a)+sin270°=​

Answer 1

1) -cot(a)x(-sin(a))-1=cos(a)/sin(a)xsin(a)-1=cos(a)-1
2) 0-1=-1

Answer 2

Let's simplify the given trigonometric expressions step by step:

1. tg(270° + a). sin(180° + a) + tg315°:

First, let's simplify tg(270° + a):

tg(270° + a) = tg(90° + a)

The tangent function has a periodicity of 180°, so we can simplify further:

tg(90° + a) = tg(90° + a - 180°) = tg(-90° + a)

Now, we can use the property that tg(-x) = -tg(x):

tg(-90° + a) = -tg(90° - a)

Next, let's simplify sin(180° + a):

sin(180° + a) = -sin(a)

Now, we have:

-tg(90° - a).(-sin(a)) + tg315°

Since tg(90° - a) is the same as tg(90° - a + 180°) due to the periodicity of the tangent function:

-tg(90° - a).(-sin(a)) = tg(90° + a).sin(a)

Now, we can rewrite the expression as:

tg(90° + a).sin(a) + tg315°

Since tg(90° + a) = -cot(a) and tg(315°) = -1, we have:

-cot(a).sin(a) - 1

2. ctg^2(360° - a)⋅cos^2(270° + a) + sin(270°):

First, let's simplify ctg^2(360° - a):

ctg^2(360° - a) = (1/tg(360° - a))^2

The cotangent function has a periodicity of 180°, so we can simplify further:

(1/tg(360° - a))^2 = (1/tg(-a))^2

Using the property that tg(-x) = -tg(x):

(1/tg(a))^2

Now, let's simplify cos^2(270° + a):

cos^2(270° + a) = sin^2(a)

Now, we have:

(1/tg(a))^2⋅sin^2(a) + sin(270°)

Since sin(270°) = -1:

(1/tg(a))^2⋅sin^2(a) - 1

So, the simplified expressions are:

1. tg(270° + a).sin(180° + a) + tg315° = -cot(a).sin(a) - 1

2. ctg^2(360° - a)⋅cos^2(270° + a) + sin(270°) = (1/tg(a))^2⋅sin^2(a) - 1