1)Find the maximum and minimum value of (1+sinA)(1+cosA)....

2)If tanA=4tanB, Find the maximum value of tan^2 (A-B)

Note - both are different questions.....!

2)If tanA=4tanB, Find the maximum value of tan^2 (A-B)

Note - both are different questions.....!

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TopNewestI'll take A=x and B=y as I like x and y more than A and B. \[1)f(x)=(1+sin x)(1+cos x)\] \[f'(x)=(cos x-sin x)(1+cos x+sin x)\] For stationary points:- \[f'(x)=0;\] \(x=\frac{\pi}{4}\) or \(x=\frac{-\pi}{2}\)

For maximum f"(x)<0 and for minimum f"(x)>0.

* So max.* \(f(x)=1.5+\sqrt2\)and min.\(f(x)=0\) \[2)x=tan^{-1}(4tan y)\] \[f(y)=tan^2(tan^{-1}(4tan y)-y)\] \[f'(y)=2tan(x-y)sec^2(x-y)(\frac{4sec^2y}{1+16tan^2y} -(-1) )\]For f'(y)=0 \[tan^2y=\frac{1}{4}\] \(tan y=\frac{1}{2}\) and \(tan x=2\) \[tan^2(x-y)=(\frac{tan x- tan y}{1+ tan x tan y})^2\] Substituting

maximum\(tan^2(x-y)= \frac{9}{16}\) – Shubham Srivastava · 4 years, 1 month agoLog in to reply

Similarly, while it is given that \( \tan x = 4 \tan y \), this does not imply that \( x = \tan^{-1} ( 4 \tan y) \), as this assumes that \(x\) lies in the principle domain. You will need to check other cases, and it seems that you simply got lucky. The answer could be very different if the condition was \( \tan 3x = \tan 4 y \), which need not imply that \(3x = 4y \). – Calvin Lin Staff · 4 years ago

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– Shubham Srivastava · 4 years ago

In such type of questions usually the domain is given in question itself. As no domain was given, so I assumed principle domain to be the domain being considered in the question.Log in to reply

I am concerned about your logical argument, and highlighting an error in your logic. Note further that the principle domain of each of the trig functions are different, and hence you are merely looking at their intersection. Your answer is thus applicable to an (arbitrary) choice of domain which is \( [0, \frac{\pi}{2} ) \). This limits its usefulness, since in part the domain excludes the minimum that you calculated.

Related: What are the maximum and minimum values of \( x + \sin x \)? – Calvin Lin Staff · 4 years ago

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thanxxxx........ – Kiran Patel · 4 years, 1 month ago

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if (1-3x)^1/2+(1-x)^5/3 (whole divided by) (4-x)........ is approximately equal to a+bx.find a and b. – Shubham Gupta · 4 years, 1 month ago

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