badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
Close

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping
Menu
Grade: 11 

                        
If A+B+C=180 prove that cotA.cotB.cotC=cotA+cotB+cotC-cosecA.cosecB.cosecC.
2 years ago

Answers : (1)

Aarushi Ahlawat
41 Points 
							
First use the given condition A+B+C=180. start with cos of both the side. after expanding the cos and sin using sum of angles identity, divide both the side by sin(A)sin(B)sin(C) and you will get the desired relation that need to be proved. Here it is how to do it:


cos(A+B+C) = cos(180)=-1


=cos(A+B)cos(C)-sin(A+B)sinC = -1


=\left (cos(A)cos(B)-sin(A)sin(B) \right )cos(C)-\left ( sin(A)cos(B)+cos(A)sin(B) \right )sin(C) = -1


=cos(A)cos(B)cos(C)-sin(A)sin(B)cos(C)-sin(A)cos(B)sin(C)-cos(A)sin(B)sin(C) = -1


 


=\frac{cos(A)cos(B)cos(C)-sin(A)sin(B)cos(C)-sin(A)cos(B)sin(C)-cos(A)sin(B)sin(C)}{sin(A)sin(B)sin(C)} =\frac{-1}{sin(A)sin(B)sin(C)}


=cot(A)cot(B)cot(C)-cot(C)-cot(B)-cot(A)=-cosec(A)cosec(B)cosec(C)


=cot(A)cot(B)cot(C)=cot(A)+cot(B)+cot(C)-cosec(A)cosec(B)cosec(C)
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Trigonometry

find the number of solutions of cosA+tanA=1,where A belongs to [0,2pi]-{pi/2,3pi/2} Answer & Earn Cool Goodies
Need to help to solve this. Totally not able to find the answer Answer & Earn Cool Goodies
5. Prove the following identities, where the angles involved are acute angles for which the...
sin 2A = 2 sin A is true when A = (A) 0° (B) 30° (C) 45° (D) 60°
State whether the following are true or false. Justify your answer. sin (A + B) = sin A + sin B.
View all Questions »


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 31 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers To Win!!! Click Here for details