Verified by Ajay Kumar
If 2 × sin q × cos(90° − q) = 1/2, where 0° < q < 90°, then find the value of sin(2q) + cos(2q).
(√2 − 1)/2
(√3 − 1)/2
(√3 + 1)/2
(√2 + 1)/2
Answer: C
Since cos(90° − q) = sin q, 2 sin² q = 1/2, giving sin² q = 1/4. As q is acute, q = 30°. Therefore, sin 60° + cos 60° = √3/2 + 1/2 = (√3 + 1)/2.
यदि 2 × sin q × cos(90° − q) = 1/2 है, जहाँ 0° < q < 90° है, तो sin(2q) + cos(2q) का मान ज्ञात करें।
(√2 − 1)/2
(√3 − 1)/2
(√3 + 1)/2
(√2 + 1)/2
उत्तर: C
cos(90° − q) = sin q होने से 2 sin² q = 1/2, अतः sin² q = 1/4। चूँकि q न्यून कोण है, इसलिए q = 30°। अतः sin 60° + cos 60° = √3/2 + 1/2 = (√3 + 1)/2।
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