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Find the maximum value of 8^{sin\Theta }\times 16^{cos\Theta }

Option: 1

16


Option: 2

64


Option: 3

32


Option: 4

128


Answers (1)

best_answer

8^{sin\Theta }\times 16^{cos\Theta }=2^{3sin\Theta}\times 2^{4cos\Theta }
=2^{3\sin\Theta+4\cos\Theta }
Maximum value of  a\sin\Theta + b\cos\Theta =\sqrt{a^{2}+b^{2}}
Maximum value of 3\sin\Theta + 4\cos\Theta =\sqrt{3^{2}+4^{2}}
=\sqrt{9+16}
=5
 maximum value of 8^{sin\Theta }\times 16^{cos\Theta }
=2^{5}
=32

Posted by

Divya Prakash Singh

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