1) \(2sin^2\theta-1=sin^4\theta-cos^4\theta\)
2) \(\frac{cos^2\theta-csc^2\theta+sin^2\theta}{sin\theta sec\theta}=-cot^3\theta\)
1)
2sin^2A - 1 = sin^4A - cos^4A
Working with the right side we can factor this as
(sin2^A + cos^2A) (sin^2A - cos^2A) =
(1) ( sin^2 A - cos^2A) =
sin^2A - (1 - sin^2A) =
sin^2A - 1 + sin^2 A =
2sin^2A - 1 which is = to the left side
2)
[ cos^2A - csc^2A + sin^2A]
_______________________ = - cot^3A
sinAsec A
Obviously...the left side is the side that needs to be simplfied
Note...... sin^2A +cos^A = 1
[ 1 - csc^2]
______________
sinA (1/cos A]
Note
cot^2A + 1 = csc^2A ....so...
1 - csc^2A = - cot^2A
-cot^2A * cosA
____________
sinA
-cot^2A * cosA
______
sin A
-cot^2A * cot A
-cot^3A which is the right side