Question

Which of the following statements is true ? Choose the correct alternative answer for multiple choice question.
(A) sinθ= cos (90-θ)
(B) cosθ= tan (90-θ)
(C) sinθ= tan (90-θ)
(D) tanθ= tan (90-θ)

Answer 1

Answer: Option (A) sinθ = cos (90-θ)

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Answer 2

Answer:

sinθ= cos (90-θ)

Step-by-step explanation:

sinθ= cos (90-θ)

is true

Let check for θ = 0°

=> Sin 0 = Cos 90 - 0

=> Sin0 = Cos90

=> 0 = 0

θ = 30

=> Sin30 = Cos(90-30)

=> Sin30 = Cos60

=> 1/2 = 1/2

cosθ= tan (90-θ) wrong

at θ = 45

Cos 45 = 1/√2

while Tan(90-45) = Tan45 = 1

1/√2 ≠ 1

sinθ= tan (90-θ) wrong

at θ = 45

Sin 45 = 1/√2

while Tan(90-45) = Tan45 = 1

1/√2 ≠ 1

tanθ= tan (90-θ) wrong

θ = 30

Tan 30  = 1/√3

Tan (90-30) = Tan60 = √3

1/√3 ≠ √3

option A  :  sinθ= cos (90-θ)   is TRUE