1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Simplify (cosec θ+cot θ)×(1−cos θ).

A
cot θ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
sec θ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
sin θ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
cosec θ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C sin θWe know that, cosec θ=1sin θ, cot θ=cos θsin θ On substituting these values, (cosec θ+cot θ)×(1−cos θ)=(1sin θ+cos θsin θ)×(1−cos θ) On multiply (1+cos θ)(1+cosθ), we get (1sin θ+cos θsin θ)×(1−cos θ)×(1+cos θ)(1+cos θ)=(1+cos θ)sin θ×(1−cos θ)×(1+cos θ)(1+cos θ)=(1+cos θ)sin θ×(1−cos2θ)(1+cos θ) By cancelling out the common terms, =(1−cos2θ)sin θ ∵ 1−cos2θ=sin2θ, on further simplifying, ⇒(1−cos2θ)sin θ=sin2θsin θ=sin θ ∴(cosec θ+cot θ)×(1−cos θ)=sin θ

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Trigonometric Ratios
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program