To simplify this expression, we first need to rewrite the trigonometric functions in terms of their basic trigonometric identities.
Recall that:
Now, let's substitute these identities into the expression:
cos(π - β) - 3sin(-3π/2) / cos(β - 3π)
= cos(π - β) - 3(-sin(3π/2)) / cos(β - 3π)
= cos(π - β) + 3sin(3π/2) / cos(β - 3π)
= -cos(β) + 3(-1) / -cos(β)
= -cos(β) - 3 / -cos(β)
= 3 + cos(β) / cos(β)
Therefore, the simplified expression is 3 + 1 / cos(β) = 4 / cos(β)
To simplify this expression, we first need to rewrite the trigonometric functions in terms of their basic trigonometric identities.
Recall that:
cos(-x) = cos(x)sin(-x) = -sin(x)Now, let's substitute these identities into the expression:
cos(π - β) - 3sin(-3π/2) / cos(β - 3π)
= cos(π - β) - 3(-sin(3π/2)) / cos(β - 3π)
= cos(π - β) + 3sin(3π/2) / cos(β - 3π)
= -cos(β) + 3(-1) / -cos(β)
= -cos(β) - 3 / -cos(β)
= 3 + cos(β) / cos(β)
Therefore, the simplified expression is 3 + 1 / cos(β) = 4 / cos(β)