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Which of the following statement true?

A] Sin q = cos (90-q) B] Cos q = tan (90-q) C] sin q

Question

Which of the following statement true?

A] Sin q = cos (90-q) B] Cos q = tan (90-q) C] sin q = tan (90-q) D] tan q = tan (90-q) pls give ans with explanation

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Mathematics
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2021-07-25T19:11:59+00:00
2021-07-25T19:11:59+00:00 2 Answers
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## Answers ( )

cos(90-q)=sin q..so,optio A

Answer:In ΔABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:

(i) Sin A, cos A (ii) sin C, cos C

Sol. In right ΔABC, we have:

p = 24 cm, b = 7 cm

2. In the figure, find tan P – cot R.

Sol. In right ΔPQR, using the Pythagoras theorem, we get

3. If sin calculate cos A and tan A.

Sol. Let us consider, the right ΔABC, we have

Perp. = BC and Hyp. = AC

4. Given 15 cot A = 8, find sin A and sec A.

Sol. Let in the right ΔABC, we have

15 cot A = 8

Now, using Pythagoras theorem, we get

5. Given calculate all other trigonometric ratios.

Sol. Let us have a right ΔABC in which ∠B = 90°

6. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Sol. Let us consider a right ΔABC,

7.

Sol. Let us have a right ΔABC in which ∠B = 90°, and ∠A = θ

8. If 3 cot A = 4, check whether

Sol. Let us consider a right angled ΔABC in which ∠B = 90°

∴For ∠A, we have:

Base = AB and Perpendicular = BC. Also Hypotenuse = AC

3 cot A = 4

9. In triangle ABC, right-angled at B, if find the value of:

(i) sin A cos C + cos A sin C (ii) cos A cos C – sin A sin C

Sol. Let us consider a right ΔABC, in which ∠B = 90°

For ∠A, we have

Base = AB

Perpendicular = BC

Hypotenuse = AC

10. In ΔPQR, right-anlged at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Sol. It is given that PQR is a right Δ, such that ∠Q = 90°

PR + QR = 25 cm

and PQ = 5 cm

Let QR = x cm

∴PR = (25 – x)

∴By Pythagoras theorem, we have

PR2 = QR2 + PQ2

⇒(25 – x) = x2 + 52

⇒625 – 50x + x2 = x2 + 25

⇒–50x = –600

11. State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than,1.

(ii) for some valued of angle A.

(iii) cos A is the abbreviation �used for the cosecant of angle A.

(iv) cot A is the product of cot and A.

(v) for some angle q.

Sol. False [∵ A tangent of an angle is ratio of sides other than hupotenuse, which may be equal or unequal to each other.]

(ii) True ∵ cos A is always less than 1

(iii) False [∵ ‘cosine A’ is abbreviated as ‘cos A’

(iv) False [‘cot A’ is a single and meaningful term whereas ‘cot’ alone has no meaning.]

(v) False [∵ is greater than 1 and sin B cannot be greater than 1.]