Math, asked by Anonymous, 6 months ago

cos A - sin A +1/
cos A +sin A-1=cosecA+cotA

Answers

Answered by JennyOreiller

2

Answer:

LHS =

(cosA-sinA)+1/(cosA+sinA)-1

Taking conjugate.

(cosA-sinA)+1/(cosA+sinA)-1 × (cosA+sinA)+1/(cosA+sinA)+1

On solving,

=cos2A-sin2A+2cosA+1/2sinAcosA

= cos2A-sin2A+2cosA+sin2A+cos2A/2sinAcosA

= 2cos2A+2cosA/2sinAcosA

= cosA+cos2A/sinAcosA

= cosA/sinAcosA +cos2A/sinAcosA

= cosecA+cotA =R.H.S

Hence, proved.

Previous Question

Next Question

Similar questions

Math, 3 months ago

3. A rectangular park is 42 m long and 36 m wide. Two cross-paths, one parallel to the length and the other parallel to the breadth, are constructed in the middle of the park. The path parallel to the length is 3 m wide and that parallel to the breadth is 2.5 m wide. Find the total area of the path.

English, 3 months ago

write an essay on the life and works of Alexander the Great. What is your personal observation about his life?

Math, 3 months ago

a) C) D d) Data inadequate DIRECTIONS (6-10): Study the following information carefully and answer the questions that follow e) There is no such teacher Madhu and Shobha are good in Dramatics and Computer Science. Anjali and adhu are good in Computer Science and Physics. Anjali, Poonam and Nisha are good in Physics and History, Nisha and Anjali are good in Physics and Mathematics. Poonam and...

English, 6 months ago

why was Valjean surprised when he was presented in front of monseigneur...

Math, 6 months ago

factorise 1+p^3 +3q^3 -6pq...

Chemistry, 10 months ago

which is the best metal for building satellites...

Math, 10 months ago

Write two rational numbers between 1/2 and 1/3...

Math, 10 months ago

the SI on a certain sum of money for 2 years at 14% per annum is 2100 find the compound interest on the sum...