Value of \sec^2 a+2\sec^2 b If a,b are 2 real number

g2esebyy7

g2esebyy7

Answered question

2022-04-19

Value of sec2a+2sec2b
If a,b are 2 real number such that 2sinasinb+3cosb+6cosasinb=7, Then sec2a+2sec2b is
Try: i am trying to sve it using cauchy schwarz inequality
[(sinb)(2sina+6cosa)+(cosb)(3)]2(sin2b+cos2b)((2sina+6cosa)2+32)
Could some help me to solve it

Answer & Explanation

icebox2686zsd

icebox2686zsd

Beginner2022-04-20Added 13 answers

Hint:
2sina+6cosa=40sin(a+x) where x=sin1640
2sinasinb+3cosb+6cosasinb=40sin(a+x)sinb+3cosb
=40sin2(a+x)+9sin(b+y)
where 40sin(a+x)=40sin2(a+x)+9cosy and 3=40sin2(a+x)+9siny
Since the maximum value of 40sin2(a+x)+9sin(b+y) is 7, we need
40sin2(a+x)+9=7 and sin(b+y)=1
The answer should be 12.

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