Question

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) बराबर है:

पर्याय

• 0

• 1

• 2

• -1

Answer 1

2

स्पष्टीकरण:

(1 + tan θ + sec θ) (1 + cot θ − cosec θ)

= `(1+ (sin theta)/(cos theta)+1/(costheta))(1+(costheta)/(sin theta)-1/(sin theta))`

= `((costheta+sintheta +1)/costheta)((sintheta+cos theta -1)/sintheta)`

= `((sintheta+costheta)^2-(1)^2)/(sinthetacostheta)`

= `(sin^2theta+cos^2 theta + 2sin theta cos theta -1)/(sinthetacostheta)`

= `(1+2sinthetacostheta -1)/(sinthetacostheta)`

= `(2sintheta costheta)/(sin theta costheta)`

= 2

अत: विकल्प 2 सही है।