Q.
If θ1,θ2,θ3,…,θn are in AP, whose common difference is d, then sin dsecθ1secθ2+secθ2secθ3+…+secθn−1secθn is equal to
see full answer
Want to Fund your own JEE / NEET / Foundation preparation ??
Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*
An Intiative by Sri Chaitanya
a
tanθn−tanθ2
b
tanθn+tanθ1
c
tanθn−tanθ1
d
None of these
answer is C.
(Unlock A.I Detailed Solution for FREE)
Ready to Test Your Skills?
Check your Performance Today with our Free Mock Test used by Toppers!
Take Free Test
Detailed Solution
Since,θ1,θ2,θ3,…,θn are in AP⇒ θ2−θ1=θ3−θ2=…=θn−θn−1=d (i)Now, taking only first termsindsecθ1secθ2=sindcosθ1cosθ2=sinθ2−θ1cosθ1cosθ2=sinθ2cosθ1−cosθ2sinθ1cosθ1cosθ2=sinθ2cosθ1cosθ1cosθ2−cosθ2sinθ1cosθ1cosθ2=tanθ2−tanθ1Similarly, we can solve other terms which will betanθ3−tanθ2,tanθ4−tanθ3,…∴sindsecθ1secθ2+secθ2secθ3+…+secθn−1secθn=tanθ2−tanθ1+tanθ3−tanθ2 +…+tanθn−tanθn−1 =−tanθ1+tanθn=tanθn−tanθ1
Watch 3-min video & get full concept clarity