Question

(1-cos square theta 1+cot square theta)
write the simplest form ​

Answer 1

(1-cos square theta 1+cot square theta)  = 1

Given,

(1-cos square theta 1+cot square theta)

= ( 1 - cos² ∅) ( 1 + cot² ∅ )

= 1 + cot² ∅ - cos² ∅ - cos² ∅ cot² ∅

= 1 + cos² ∅/sin² ∅ - cos² ∅ - cos² ∅ ( cos² ∅/sin² ∅ )

= ( 1 - cos² ∅ ) + cos² ∅/sin² ∅ - (cos² ∅ × cos² ∅) /sin² ∅

= sin² ∅ + cos² ∅ ( 1 - cos² ∅ ) /sin² ∅

= sin² ∅ + cos² ∅ ( sin² ∅ ) /sin² ∅

= sin² ∅ + cos² ∅ (1)

= sin² ∅ + cos² ∅

= 1