1. (sin θ - cos θ)^2
2. sec^2 θ - tan^2 θ - sin^2 θ
Can you please show the step by step process of how to simply both? Please and thank you!
1. (sin θ - cos θ)^2
= (sin θ)^2 - 2sinθcosθ + (cos θ)^2
= sin^2 θ - 2sinθcosθ + cos^2 θ
= 1 - 2sinθcosθ
2. sec^2 θ - tan^2 θ - sin^2 θ
= (1/cos^2 θ) - (sin θ/cos θ)^2 - (sin θ)^2
= 1 - (sin θ/cos θ)^2 - (sin θ)^2
= 1 - (sin^2 θ/cos^2 θ) - (sin^2 θ)
= 1 - (sin^2 θ + sin^2 θ/cos^2 θ)
= 1 - (sin^2 θ(1 + 1/cos^2 θ))
= 1 - sin^2 θ(sec^2 θ)
= 1 - sin^2 θsec^2 θ
1.
one more step ....
1 - 2sinθcosθ
= 1 - sin 2θ
2.
sec^2 θ - tan^2 θ - sin^2 θ
= (tan^2 θ + 1) - tan^2 θ - sin^2 θ , since sec^2 θ = tan^2 θ + 1
= 1 - sin^2 θ
= cos^2 θ