Question

1)sin^2(180-a)= 2)tg(5п/2-а)=

Answer 1

1) sin^2(180°-a)= sin^2 a;
2) tg (5п/2-а)= tg(п/2-а)= ctg a.

Answer 2

1. To simplify sin^2(180-a):

Recall the trigonometric identity: sin^2(x) + cos^2(x) = 1

Since sin^2(x) + cos^2(x) = 1, we can rearrange it to get sin^2(x) = 1 - cos^2(x).

Now, let's use the angle subtraction formula for cos:

cos(180 - a) = -cos(a)

Substitute this into sin^2(180-a):

sin^2(180-a) = 1 - cos^2(180-a) = 1 - (-cos^2(a)) (using cos(180 - a) = -cos(a)) = 1 + cos^2(a)

So, sin^2(180-a) = 1 + cos^2(a).

2. To find tg(5п/2-а):

Recall that tg(x) (also written as tan(x)) is the tangent function, which is defined as tan(x) = sin(x) / cos(x).

Let's find sin(5π/2 - a) and cos(5π/2 - a):

sin(5π/2 - a) = sin(π/2 - a) (5π/2 is equivalent to 2π, so we can subtract 2π from it) = cos(a) (using the complementary angle property)

cos(5π/2 - a) = cos(π/2 - a) (5π/2 is equivalent to 2π, so we can subtract 2π from it) = sin(a) (using the complementary angle property)

Now, we can find tg(5π/2 - a):

tg(5π/2 - a) = sin(5π/2 - a) / cos(5π/2 - a) = cos(a) / sin(a)

So, tg(5π/2 - a) = cos(a) / sin(a).