Scroll:Trigonometry >> Prove the identity >> ps (4126)
Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1)
Answer:_______________ |
| 2) If x= a secØ + b tanØ and y= a tanØ + b secØ, then prove that x2 - y2 = a2 - b2
Answer:_______________ |
| 3) Determine whether each of the following is an identity or not.
Answer:_______________ |
| 4) prove that,
Answer:_______________ |
| 5) Prove the following, Ø Ø Answer:_______________ |
| 6) determine whether each of the following is an identity or not. Answer:_______________ |
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| 7) Prove that,
Ø Ø 2Ø Answer:_______________ |
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| 8) Answer:_______________ |
| 9) Prove the identity,
Answer:_______________ |
| 10)
Answer:_______________ |
| 1)
Answer: 2 |
| 2) If x= a secØ + b tanØ and y= a tanØ + b secØ, then prove that x2 - y2 = a2 - b2
Answer: 2 SOLUTION 1 :
TO PROVE: x2 - y2 = a2 - b2 PROOF: L.H.S. = x2 - y2 =(a sec Ø + b tan Ø ) - (a tanØ + b secØ )2 =[(a secØ ) + 2(a secØ ) (b tanØ ) + (b tanØ )2] - [(a tanØ )2 + 2 (a tanØ ) (b sinØ ) + (b sec Ø)2] = (a2 sec2Ø+ 2 ab secØ tanØ + b2 tan2 Ø) -(a2 tan2Ø+ 2 ab tanØ secØ + b2 sec2Ø) = ( a2 sec2 Ø+ 2 ab secØ tanØ + b2 tan2Ø) - (a2 tan2 Ø - 2 ab tanØ secØ + b2 sec2Ø) = a2 sec2Ø- a2 tan2 Ø _ b2 tan2Ø- b2 sec2Ø
= a2 (sec2Ø - tan2Ø) - b2 (sec2 Ø- tan2Ø)
=a2 (1) - b2 (1) =a2 - b2 = RHS so R.H.S = L.H.S Hence proved. |
| 3) Determine whether each of the following is an identity or not.
Answer: 2 |
| 4) prove that,
Answer: 1 |
| 5) Prove the following, Answer: tanØ Answer: cotØ |
| 6) determine whether each of the following is an identity or not. Answer: 1 |
| 7) Prove that,
Answer: 1-2secØ Answer: tan Ø Answer: 2tan2Ø |
| 8) |
| 9) Prove the identity,
Answer: 1 |
| 10)
Answer: 1 |