Q.

If θ1,θ2,θ3,…,θn are in AP, whose common difference is d, then  sin⁡ dsec⁡θ1sec⁡θ2+sec⁡θ2sec⁡θ3+…+sec⁡θn−1sec⁡θn 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

tan⁡θn−tan⁡θ2

b

tan⁡θn+tan⁡θ1

c

tan⁡θn−tan⁡θ1

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 termsin⁡dsec⁡θ1sec⁡θ2=sin⁡dcos⁡θ1cos⁡θ2=sin⁡θ2−θ1cos⁡θ1cos⁡θ2=sin⁡θ2cos⁡θ1−cos⁡θ2sin⁡θ1cos⁡θ1cos⁡θ2=sin⁡θ2cos⁡θ1cos⁡θ1cos⁡θ2−cos⁡θ2sin⁡θ1cos⁡θ1cos⁡θ2=tan⁡θ2−tan⁡θ1Similarly, we can solve other terms which will betan⁡θ3−tan⁡θ2,tan⁡θ4−tan⁡θ3,…∴sin⁡dsec⁡θ1sec⁡θ2+sec⁡θ2sec⁡θ3+…+sec⁡θn−1sec⁡θn=tan⁡θ2−tan⁡θ1+tan⁡θ3−tan⁡θ2 +…+tan⁡θn−tan⁡θn−1 =−tan⁡θ1+tan⁡θn=tan⁡θn−tan⁡θ1
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon