Question

Evaluate cot theta .tan(90- theta)-sec(90- theta) cosec theta + ( sin 2 35 + sin 2 55) + root 3(tan 5.tan 15.tan 30 .tan 75.tan 85)

Answer 1

cotθ.tan(90°-θ)-sec(90°-θ)cosecθ+(sin²35°+sin²55°) +√3(tan5°.tan15°.tan30°.tan75°.tan85°)
=cotθ.cotθ-cosecθ.cosecθ+sin²35°+sin²(90°-35°)+√3{tan5°.tan15°.(1/√3).
tan(90°-15°).tan(90°-5°)}
=cot²θ-cosec²θ+sin²35°+cos²35°+√3×1/√3(tan5°tan15°cot15°cot5°)
=-1+1+{tan5°tan15°(1/tan15°)(1/tan5°)}
=1

Answer 2

Answer:

cotθ.tan(90°-θ)-sec(90°-θ)cosecθ+(sin²35°+sin²55°) +√3(tan5°.tan15°.tan30°.tan75°.tan85°)

=cotθ.cotθ-cosecθ.cosecθ+sin²35°+sin²(90°-35°)+√3{tan5°.tan15°.(1/√3).

tan(90°-15°).tan(90°-5°)}

=cot²θ-cosec²θ+sin²35°+cos²35°+√3×1/√3(tan5°tan15°cot15°cot5°)

=-1+1+{tan5°tan15°(1/tan15°)(1/tan5°)}

=1