Question

Trigonometric identities: Performance task

Answer 1

Answer:

1) sin²x

2) 1

Step-by-step explanation:

1) (1+cos x)(1-cos x)

=> 1-cos²x

=> sin²x

2) 1/cot²x -1/cos²x

=> tan²x-sec²x

=> 1

Answer 2

#1

$\\ \sf\longmapsto (1+cosx)(1-cosx)$

$\\ \sf\longmapsto 1-cos^2x$

$\\ \sf\longmapsto sin^2x$

#2

$\\ \sf\longmapsto \dfrac{1}{cot^2x}-\dfrac{1}{cos^2x}$

$\\ \sf\longmapsto tan^2x-sec^2x$

$\\ \sf\longmapsto 1$