To simplify the given expression, we need to combine all terms into a single trigonometric function.
Let's start by converting the trigonometric functions to their respective identities.
5/cosx - 2/sinx = 10/sin2x
Firstly, we need to express sin2x in terms of sinx and cosx.
sin2x = 2sinxcosx
Substitute back into the equation:
5/cosx - 2/sinx = 10/(2sinxcosx)
Now, combine the terms on the right side:
5/cosx - 2/sinx = 5/(sinx * cosx)
Now, we need to find the least common denominator, which is sinx * cosx:
(5sinx - 2cosx)/(sinx cosx) = 5/(sinx cosx)
Now, cross multiply:
5sinx - 2cosx = 5
Rearrange the equation to isolate one of the variables:
5sinx = 5 + 2cosx
Divide by 5:
sinx = (5 + 2cosx) / 5
Therefore, the simplified form of the given expression is sinx = (5 + 2cosx) / 5.
To simplify the given expression, we need to combine all terms into a single trigonometric function.
Let's start by converting the trigonometric functions to their respective identities.
5/cosx - 2/sinx = 10/sin2x
Firstly, we need to express sin2x in terms of sinx and cosx.
sin2x = 2sinxcosx
Substitute back into the equation:
5/cosx - 2/sinx = 10/(2sinxcosx)
Now, combine the terms on the right side:
5/cosx - 2/sinx = 5/(sinx * cosx)
Now, we need to find the least common denominator, which is sinx * cosx:
(5sinx - 2cosx)/(sinx cosx) = 5/(sinx cosx)
Now, cross multiply:
5sinx - 2cosx = 5
Rearrange the equation to isolate one of the variables:
5sinx = 5 + 2cosx
Divide by 5:
sinx = (5 + 2cosx) / 5
Therefore, the simplified form of the given expression is sinx = (5 + 2cosx) / 5.