Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Prove that
(i) (cosec θ – sin θ ) (sec θ – cos θ ) (tan θ + cot θ ) = 1
(ii) 
= 
(iii) 
= ± (sec A – tan A)
(iv) 
= cosec A – sec A
(v) 
– 
= 
– 
(vi) 
+ 
= 2
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(i)L.H.S = (cosec θ – sin θ ) (sec θ – cos θ ) (tan θ + cot θ )
= 
= 
= 1 = RHS
(ii)LHS = 
= 
= 
= 
= RHS
(iii)LHS = 
= 
= 
= ± (secA – tanA) = RHS.
(iv) 
= 
(v) 
= 
Now taking RHS 
= 
(vi) 
cos 2 A + sin 2 A – sinA cosA + cos 2 A + sin 2 A + sin A cosA = 2
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Show that :
(i) sin 2 75 ° – sin 2 15 ° =
(ii) sin 2 45 ° – sin 2 15 ° =
If α and β are the solution of a cos θ + b sin θ = c, then show that cos( α + β ) =
Show that : sin 2 – sin 2 = sin A
Show that : cos² α + cos² ( α + β ) − 2cos α cos β cos ( α + β ) = sin² β .
Prove that
(i) = tan (A + B)
(ii) cot (A + 15 º ) – tan (A – 15 º ) =
If 0 < θ < π /4, then show that = 2 cos θ