Q1
Write LHS in terms of sin and cos
Get a common denominator and add
You should recognise and simplify the top
Split up the product
You should now have the RHS
TRY IT!!
Q2 Hint: a^4 - b^4 =(a^2 + b^2)(a^2 - b^2)
The first bracket will be =1
Look at the RHS (there is no cos in sight!)
So, replace (cos x)^2 with 1 - (sin x)^2
Too easy!
Q3 Use the identity 1 + (cot x)^2 = (cosec x)^2 on the bottom
Dividing by (cosec x)^2 is the same as multiplying by (sin x)^2
So now you should have (sin x)^2 x ((cot x)^2 -1)
Write cot^2 in terms of sin and cos
Expand out bracket
Do the same thing you did at the end of Q2 to get rid of cos^2
Done