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don't understand how to solve these 3 questions from my homework, please help?
1. Use the given values to evaluate(if possible) the remaining trigonometric functions. Given: sin theta=2/sqrt 5 and cos theta=1/sqrt 5.
2. Verify the identity (1-2 sin^2 theta)/(sin theta cos theta)=cos theta-tan theta
3. Solve the equation sin theta cos theta=-1/2 on the interval [0,2pi).
Im taking theta as x as theta is too long to type
Sinx = 2/root(5)
Cosx=1/root(5)
Tanx = sinx /cosx = 2
Secx= 1/cosx= root(5)
Cosecx = 1/sinx = root5/2
Cotx= 1/tanx = 1/2
There goes the first one
Ur second q is wrong
U get the ans as cot x-tanx not cosx-tanx
1-2sin^2x)/sinx cosx
Cos^2x+sin^2x -2sin^2X )/SINXCOSX
Cos^2x -sin^2x /sinxcosx
Dividing numerator by denominator
Divide term by term
Cotx-tanx
There's the second
Third im not really sure
But I guess it's likee this
Sinxcosx =-1/2
Sin2x/2 = -1/2 (sin2x = 2sinxcosx (standard result
Sin2x = -1
2x = 3pi/2(sin3pi/2 = -1
X = 3pi/4
Just check if thats the ans
I hope that helped
