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## Important Formulas and Questions

Q1) If sec θ + tan θ = 2, what is the value of sec θ?

1)
3/2
2) 5/2
3) 2
4) 5/4

sec2θ - tan2θ = 1
(sec θ - tan θ)(sec θ + tan θ) = 1
sec θ - tan θ = 1/2
sec θ + tan θ = 2 (Given in the question)
2sec θ = 5/2
So, sec θ = 5/4
Hence, option 4.

Q2) If sec ⁡θ - cosec θ = 0 then the value of tan ⁡ θ + cot ⁡θ is

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

sec ⁡θ - cosec θ = 0
sin ⁡ θ = cos ⁡θ
tan ⁡ θ = 1
tan ⁡ θ + cot ⁡ θ = tan ⁡θ + 1/tan ⁡θ = 1 + 1 = 2

Hence, option 4.

Q3) If then the value of is

1)
0
2) 1/3
3) 2/3
4) 4/3

Hence, option 3.

Trigonometric Identities
Q4) If tan ⁡ θ = 4/3 then the value of is

1)
0.5
2) -0.5
3) 3
4) -3

Hence, option 3.

Q5) If sec2θ + tan2θ = 7/12 then sec4θ - tan4θ is equal to

1)
7/12
2) 1/2
3) 5/12
4) 1

sec4θ - tan4θ = (sec2θ + tan2θ)(sec2θ - tan2θ) = 7/12
Hence, option 1.

Q6) The value of tan 1°.tan 2°.tan 3°---tan 89°

1)
0
2) 1
3) 89
4) undefined

tan ⁡a . tan ⁡b = 1 where a + b = 90°
tan 1°.tan 2°.tan 3°---tan 89° = 1
Hence, option 2.

Q7) If A = tan 11°.tan 29°, B = 2 cot 61°.cot 79° then

1)
A = 2B
2) 2A = B
3) -2A = B
4) A = -2B

B = 2 cot 61°.cot 79°
B = 2 cot(90 - 29)°cot(90 - 11)°
B = 2 tan 11°.tan 29°
B = 2A
Hence, option 2.

Q8) If α, β and γ are acute angled such that sin α = sqrt(3)/2 = cos β and tan γ = 1, then what is α + β + γ is equal to?

1)
105°
2) 120°
3) 135°
4) 150°

sin α = sqrt(3)/2 i.e. α = 60°
cos β = sqrt(3)/2 i.e. β = 30°
tan γ = 1 i.e. γ = 45°
α + β + γ = 60° + 30° + 45° = 135°
Hence, option 3.

Q9) If tan 7θ tan 2θ = 1, then the value of tan3θ is

1)
sqrt(3)
2) -1/sqrt(3)
3) 1/sqrt(3)
4) -sqrt(3)

tan 7θ tan 2θ = 1
tan 7θ = cot 2θ
tan 7θ = tan(90° - 2θ)
7θ = 90° - 2θ
9θ = 90°
θ = 10°
tan 3θ = tan 30° = 1/sqrt(3)
Hence, option 3.

Q10) What is the value of sin A cos A tan A + cos A sin A cot A

1)
sin2A + cos A
2) sin2A + tan2A
3) sin2A + cot2A
4) cosec2A - cot2A

sin A cos A tan A + cos A sin A cot A
= sin2A + cos2A = 1
cosec2A - cot2A
Hence, option 4.