Question

Решите пожалуйста: 1) a tg x=sin x 2) ctg x=a cos x3) a sin x=1 4) a sin 2x=cos x​

Answer 1

1) a = sin(x)/tg(x)

tg(x)=sin(x)/cos(x)

a = sin(x)*cos(x)/sin(x)

a=cos(x)

2) a= ctg(x)/cos(x)

ctg(x) = cos(x)/sin(x)

a= cos(x)/sin(x)*cos(x)

a=1/sin(x)

3) a=1/sin(x)

4) a=cos(x)/sin(2x)

sin(2x) = 2sin(x)*cos(x)

a=cos(x)/2sin(x)*cos(x)

a=1/2sin(x)

 

Answer 2

1) a tg x = sin x Applying the trigonometric identity for tangent, we get: a sin x / cos x = sin x Dividing both sides by sin x, we get: a / cos x = 1 Therefore, a = cos x

2) ctg x = a cos x Using the reciprocal identity for cotangent, we get: 1 / tan x = a cos x Substituting tan x = sin x / cos x, we get: cos x / sin x = a cos x Dividing both sides by cos x, we get: 1 / sin x = a Therefore, a = 1 / sin x

3) a sin x = 1 Dividing both sides by sin x, we get: a = 1 / sin x

4) a sin 2x = cos x Using the double angle identity for sine, we get: 2a sin x cos x = cos x Dividing both sides by cos x, we get: 2a sin x = 1 Therefore, a = 1 / (2 sin x)