If cos x = sin(20+x) degrees and 0 degrees < x < 90 degrees, the value of x is

x = 35°

Step-by-step explanation:

From the question given above:

cos x = sin(20 + x)

The value of x can be obtained as follow:

cos x = sin(20 + x)

Recall:

sin(A + B) = sinAcosB + cosAsinB

Therefore,

sin(20 + x) = sin20cosx + cos20sinx

cos x = sin(20 + x)

cos x = sin20cosx + cos20sinx

Collect like terms

cos x – sin20cosx = cos20sinx

cos x(1 – sin20) = cos20sinx

Divide both side by cosx

(1 – sin20) = cos20sinx / cosx

Recall:

Tan x = sinx / cosx

(1 – sin20) = cos20tanx

Divide both side by cos20

(1 – sin20) / cos20 = tanx

(1 – 0.3420) / 0.9397 = tanx

0.658 / 0.9397 = tanx

0.7 = tanx

Take the inverse of tan

x = tan¯ 0.7

x = 35°

2nd one in the first row is correct

570, the answer is 570, hope it