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CLASS XMATHEMATICS
(2023 – 24)
PRACTICE QUESTIONS: SET 5
Section A
Answer ALL the following Questions. Each question carries 2 marks.
cot2 𝑥
1. Show that 1 + = 𝑐𝑜𝑠𝑒𝑐 𝑥, 0° < 𝑥 < 90°
1+𝑐𝑜𝑠𝑒𝑐 𝑥
sinx−cosx
2. If 3 𝑐𝑜𝑡𝑥 = 2, find the value of
sinx+cosx
3. If the angles of a triangle ABC are in the ratio 1 ∶ 2 ∶ 3 (largest angle being angle C), then
sec A tan 𝐴
find the value of − .
cosec B cot 𝐵
4. ΔABC is right-angled at C. If AB = 29 cm, BC = 21 cm, ∠ABC = x, find the value of
cos2𝑥 − sin2𝑥.
5. If tan245o − cos230o = 𝑥 sin45o cos45o, find 𝑥.
6. A circus artist is climbing from the ground along a rope stretched from the top of a vertical
pole and tied at the ground. The height of the pole is 12 m and the angle made by the rope
with ground level is 30°. Calculate the slant distance covered by the artist in climbing to the
top of the pole. You may assume that there is no slack in the rope.
Section B
Answer ALL the following Questions. Each question carries 3 marks.
7. If 1 + sin2 𝑥 = 3 sin 𝑥 cos 𝑥, find the values of tan 𝑥.
8. If 𝑥 = 𝑎 sec 𝐴 + 𝑏 tan 𝐴 and 𝑦 = 𝑎 tan 𝐴 + 𝑏 sec 𝐴, prove that, 𝑥2 − 𝑦2 = 𝑎2 − 𝑏2.
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