- A-1
- B0
- C2
- D1
Step-by-Step Solution
cos 52° = sin 38° and sin 52° = cos 38°. So expression = cos 38°·sin 38° − sin 38°·cos 38° = 0.
Answer: B) 0
Simplify: cos 38° · cos 52° − sin 38° · sin 52°. (Hint: 38° and 52° are complementary.)
Class 10Introduction to TrigonometryTrigonometry
Key idea: Complementary angle identities
Since the two acute angles of a right triangle sum to 90° (complementary), the side that is 'opposite' to one angle is 'adjacent' to the other. This swaps sine and cosine:
**sin(90° − θ) = cos θ**
**cos(90° − θ) = sin θ**
**tan(90° − θ) = cot θ**
**cot(90° − θ) = tan θ**
**sec(90° − θ) = csc θ**
**csc(90° − θ) = sec θ**
**Use**: simplify expressions like sin 70° = cos 20°, cos 80° = sin 10°. Also useful in proof-style questions: 'Show sin 25° / cos 65° = 1.'
**sin(90° − θ) = cos θ**
**cos(90° − θ) = sin θ**
**tan(90° − θ) = cot θ**
**cot(90° − θ) = tan θ**
**sec(90° − θ) = csc θ**
**csc(90° − θ) = sec θ**
**Use**: simplify expressions like sin 70° = cos 20°, cos 80° = sin 10°. Also useful in proof-style questions: 'Show sin 25° / cos 65° = 1.'
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If sin A = 1/2, what is the value of 3 cos A − 4 cos³A? (A is acute.)The maximum value that sin θ can take is:Assertion (A): tan(90° − θ) = cot θ. Reason (R): In a right triangle the two acute…In right triangle PQR, right-angled at Q, PQ = 9 cm, QR = 12 cm and PR = 15 cm. A…In right triangle ABC, right-angled at C, AC = 9 cm and BC = 40 cm. Find cot A.