Question

The minimum value of 7^sinq + 7^cosq is equal to

• A. $2 \times 7^{- 1/\sqrt{2}}$
• B. 2 × $7^{\sqrt{2}}$
• C. $2 \times 7^{1/\sqrt{2}}$
• D. $2 \times 7^{- \sqrt{2}}$

Answer 1

Answer: (A)

$2 \times 7^{- 1/\sqrt{2}}$

Answer 2

AM ³ GM

7^sinq + 7^cosq ³ 2$\sqrt{7^{\sin\theta}.7^{\cos\theta}}$

³ 2 × $7^{\frac{\sin\theta + \cos\theta}{2}}$

³ 2 × $7^{- \frac{1}{\sqrt{2}}}$