Question

Sin (90° – A) and cos A are: *
1 point
Not related
Same
None of the above
Different

Answer 1

Answer:

Same/Equal

Step-by-step explanation:

We know that,

CosA = Sin(90 - A)

Let's Prove it first,

Let ΔABC be a right triangle, right angled at C

Now, We know that,

∠A + ∠B + ∠C = 180° (Angle Sum Property)

But we know that ∠C = 90°

So,∠A + ∠B = 180 - 90 = 90°

∠B = 90° - ∠A

So, the angles in our triangle becomes ∠A, (90 - ∠A), ∠C.

Now,

CosA = AC/AB (Adj./Hypo.) [In our triangle]

Sin(90 - A) = AC/AB (Opp./Hypo)

Now, From above we get,

CosA = Sin(90 - A) = AC/AB

Thus,

Cos A = Sin (90 - A)

Thus, CosA and Sin(90 - A) are same

Hope it helped and you understood it........All the best

Answer 2

Answer:

We know the trigonometric identity

sin (A – B) = sin A.cos B – sin B.cos A

Hence substituting A= 90 and B= A in the above identity. We get

sin (90 – A) = sin 90.cos A – sin A cos 90.

We have learnt that sin 90 = 1, And cos 90 = 0

sin (90 – A) = cos A

correct answer : option b same