Answer:
b. csc x
Step-by-step explanation:
cos x cotx + sin x
We know that cot = cos/sin
cos x cos x/ sin x + sin x
cos^x /sin x + sin x
Getting a common denominator of sin x
cos^2 x /sin x + sin x * sin x / sin x
cos ^2 x / sin x + sin^2 x / sin x
( cos ^2 x + sin^2 x) / sin x
We know that cos ^2 x + sin^2 x = 1
1 / sin x
We know that 1 / sin x = csc x
csc x
Answer:
b. csc x
Step-by-step explanation:
To simplify the expression;
cos x cotx + sinx
But cot x = [tex]\frac{cos x}{sinx}[/tex]
Substitute cot x = [tex]\frac{cos x}{sinx}[/tex] into the initial expression
cos x cotx + sinx
= [tex]cos x. \frac{cos x}{sinx} + sin x[/tex]
= [tex]\frac{cos^{2} x}{sinx} + sin x[/tex]
= [tex]\frac{cos^{2} x + sin^{2}x }{sin x}[/tex] But [tex]sin^{2}x + cos^{2}x = 1[/tex]
= [tex]\frac{1}{sinx}[/tex] But [tex]\frac{1}{sinx}[/tex]= cosec x
= cosec x
Therefore, cos x cotx + sinx = cosec x
