Test: Sum & Difference Formula - JEE MCQ

# Test: Sum & Difference Formula - JEE MCQ

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## 15 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Sum & Difference Formula

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Test: Sum & Difference Formula - Question 1

### sin 51° + cos 81° = ?

Detailed Solution for Test: Sum & Difference Formula - Question 1

Test: Sum & Difference Formula - Question 2

### cos9y - cos5y =

Detailed Solution for Test: Sum & Difference Formula - Question 2

cosC - cosD = 2sin (C+D)/2 sin(D -C)/2
cos9y - cos5y = 2sin(9y+5y)/2 sin(5y-9y)/2
= 2 sin (14y/2) sin(-4y/2)
= 2 sin7y sin(-2y)
= - 2 sin7y sin2y

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Test: Sum & Difference Formula - Question 3

### What is the value of sin 35θ – sin55θ?

Detailed Solution for Test: Sum & Difference Formula - Question 3

sinA - sinB = 2cos(A+B)/2 sin(A-B)/2
sin 35 – sin55 = 2cos(35+55)/2 sin(35-55)/2
= 2cos45 (-sin10)
= 2(√2/2) (-sin10)
= -√2 sin10

Test: Sum & Difference Formula - Question 4

Sin25sin55= ?

Detailed Solution for Test: Sum & Difference Formula - Question 4

sin25° sin55°
Multiply and divide by '2'
1/2(2 sin25° sin55°)
cos(a-b) + cos(a+b) = 2sina sinb
1/2[cos(a-b) - cos(a+b)] = sina sinb
1/2[cos(25° - 55°) - cos(25° + 55°)] = sin25° sin55°
1/2[cos(-30°) - cos(80°)] = sin25° sin55°
1/2[cos(30°) - cos(80°)] = sin25° sin55°

Test: Sum & Difference Formula - Question 5

Detailed Solution for Test: Sum & Difference Formula - Question 5

Test: Sum & Difference Formula - Question 6

In a triangle ABC, cosA - cosB =

Detailed Solution for Test: Sum & Difference Formula - Question 6

Test: Sum & Difference Formula - Question 7

cosA + cos (120° + A) + cos(120° – A) =

Detailed Solution for Test: Sum & Difference Formula - Question 7

CosA + Cos(120o-A) + Cos(120°+A)
cosA + 2cos(120° - a + 120° + a)/(2cos(120° - a - 120° - a)
we know that formula
(cos C+ cosD = 2cos (C+D)/2.cos (C-D) /2)
⇒ cosA + 2cos120° cos(-A)
⇒ cosA+ 2cos (180° - 60°) cos(-A)
⇒ cosA + 2(-cos60°) cosA
⇒ cos A - 2 * 1/2cos A
⇒ cosA-cosA
⇒ 0

Test: Sum & Difference Formula - Question 8

What is the value of cos 1050  + cos750 ?

Detailed Solution for Test: Sum & Difference Formula - Question 8

cos105° + cos75°
= cos(90º + 15) + cos(90° - 15)
= - sin15 + sin15 = 0

Test: Sum & Difference Formula - Question 9

In a triangle ABC, if angle A = 72° , angle B = 48° and c = 9 cm then Ĉ is

Test: Sum & Difference Formula - Question 10

Value of cos35cos450 is

Detailed Solution for Test: Sum & Difference Formula - Question 10

cos35o cos45o
Multiply and divide numerator and denominator by 2
1/2{2cos35o cos45o}
= 1/2{cos(35o+45o) + cos(35o-45o)}
= 1/2{cos80o + cos(-10o)}    { cos(-x) = cosx
= {cos80o + cos10o}/2

Test: Sum & Difference Formula - Question 11

cosA - cos3A =

Test: Sum & Difference Formula - Question 12

Detailed Solution for Test: Sum & Difference Formula - Question 12

sin(A+B)-sin(A-B) = 2cosAsinB
= 2cos(π/4)sinX
= 2 × 1/√2 sin X
= √2sinX

Test: Sum & Difference Formula - Question 13

sin (n+1)x cos(n+2)x - cos(n+1)x sin(n+2)x =

Detailed Solution for Test: Sum & Difference Formula - Question 13

sin(n+1)x cos(n+2)x - cos(n+1)x sin(n+2)x
⇒ sin[(n+1)x - (n+2)x]
As we know that sin(A-B) = sinA cosB - cosA sinB
⇒ sin(n+1-n-2)
sin(-x)
= -sinx

Test: Sum & Difference Formula - Question 14

cos 15° – sin 15° = ?

Detailed Solution for Test: Sum & Difference Formula - Question 14

cos 15o - sin 15o
= cos(45o - 30o) - sin(45o - 30o)
= (cos45ocos30o + sin45osin30o) - (sin45ocos30o - cos45osin30o)
= [√3/(2√2) + 1/(2√2)] - [√3/(2√2) - 1/(2√2)]
= 2/(2√2)
= 1/√2

Test: Sum & Difference Formula - Question 15

Find the value of cos180 + sin360

## Mathematics (Maths) for JEE Main & Advanced

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests