The value of cosec(67° + θ) - sec(23°- θ) + cos15°cos35°cosec55°cos60°cosec75° is ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1/2.
We know that,
cos (x)- sec (y)=0 , if [x° + y° =90°]
so,
= cosec(67° + θ) - sec(23°- θ ) = 0
= cos15° cos35° cosec55° cos60° cosec75°
= cos15° cos35° sec35° cos60° sec15° [as cosec (90 - θ)=sec θ ]
= cos15°sec15° cos35° sec35° cos60°
= cos 60° [ cos θ secθ =1]
= 1/2