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## SSC 2015 paper questions

Q11) If 0° < θ < 90° then the value of sin θ ⁡ + cos ⁡θ is

1) equal to 1
2) greater than 1
3) less than 1
4) equal to 2

Let y = sin ⁡ θ + cos ⁡θ
y2 = sin2⁡ θ + cos2⁡θ + 2 sinθ.cos⁡θ
= 1 + 2sin⁡θcos⁡θ
For 0° < θ < 90°,sin⁡θ < 1,cos⁡θ < 1
2 sin ⁡θ cos ⁡θ < 1
y2 = 2
y < √2
Hence, option 3.

Q12) Maximum value of sin8θ + cos14θ for all real values of θ is

1) 1
2) 0
3) 1.414
4) 0.707

sin8θ + cos14θ = sin8θ + (1 - sin2θ)7
Maximum value of sin2θ = 1
So, maximum value of sin8θ + (1 - sin2θ)7 = 1 + 0 = 1
Hence, option 1.

Trigonometric Identities
Q13) If then the value of is

1) -1
2) 0
3) 1
4) 2  for all integral values of x. Hence, option 2.

Q14) In a right angled triangle XYZ right angled at Y, if then sec x + tan x is  Hence, option 2.

Q15) If cos ⁡ x + sec ⁡x = 2 then what is the value of cos(n+1)⁡ x + sec(n+1)⁡x where n is a positive integer?

1) 2(n+1)
2) 2(n-1)
3) 2n
4) 2 If then So, cos(n+1)⁡ x + sec(n+1)⁡x = 2
Hence, option 4.

Q16) Consider the following statements
A) tan ⁡θ increases faster than sin ⁡θ as θ increases.
B) The value of sin θ ⁡ + cos ⁡θ is always greater than 1.
Which of the statements given above is/are correct?

1) Only A
2) Only B
3) Both A and B
4) Neither A nor B

Statement A is correct as tan θ ⁡ increases faster than sin ⁡θ as θ increases.
Statement B is not correct as sin θ ⁡ + cos ⁡θ can even be equal to 1.
Hence, option 1.

Q17) If where 0° < θ < 90° then tan θ is equal to   Hence, option 3.

Q18) If cos ⁡x + cos2x = 1 then the numerical value of sin12x + 3sin10x + 3sin8x + sin6x - 1 is

1) 1
2) 0
3) -1
4) 2

cos ⁡ x + cos2x = 1
cos ⁡ x = 1 - cos2x = sin2x
On cubing both sides,
cos ⁡x + cos2x = 1
(cos ⁡x + cos2x)3 = 1
cos6x + 3cos5x + 3cos4x + cos3x = 1
Put cos ⁡x = sin2x
sin12x + 3sin10x + 3sin8x + sin6x = 1
sin12x + 3sin10x + 3sin8x + sin6x - 1 = 0
Hence, option 2.