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 About the author Adalynn
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.] Reply
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.]