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solve these in detail plz : 1)the minimum value of sec²x + cosec²x is ....??? 2)If the max value of cos(cosx) is a and min value is b then b= cos a a =cos b a = 0 b =0 plz explain me how to do questions like this with a good and faster approach..


solve these in detail plz :


1)the minimum value of sec²x + cosec²x is ....???


2)If the max value of cos(cosx) is a and min value is b then



  1.  b= cos a

  2. a =cos b

  3. a = 0

  4. b =0

plz explain me how to do questions like this with a good and faster approach.. 

Grade:12

2 Answers

Tushar Makkar
37 Points
12 years ago

write sec^2 x and cosec^2 x in terms of cos and sine ...

take common denominator

apply cos^2 x + sin^2 x =1;

multiply deno. and numerator by 4 

apply sin2x= 2sinx cos x in denominator

u'll get 4/(sin2x)^2

min. value of this term is when deno. is max. which is 1 so ans. is 4,,,,....

plz. approve the ans

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
12 years ago

Hello abhijat !

 

Well In case when trignometric function comes in picture...try to reduce in form of a single trignometric function like sinx and cox...because it is known to you that max and minimum value of sin or cos is 1 and -1 ...hence question becomes a bit easier...well i am solving the first one first...

 

1) sec^2x + cosec^2x

 

1/sin^2x + 1/cos^2x

 

taking LCM and solving it ..     (sin^2x+cos^2x)/(sinx.cosx)^2

 

--------------------------------=  1/(sinx.cosx)^2

multiply by 4 up and down ..=  4/(2sinx.cosx)^2

so ....................................= 4/sin^2x

 

For the minimum value of this expression sin^2x should be maximum ..and hence it comes 4 ...

 

 

Question 2 :

 

Cos(cosx)  ---?

 

Well cosx has maximum value equal to 1 only if  x is 0 or 2pi...or multiple of 2pi ...

and the minimum value of cosx is equal to -1 only if x is pi ..or multiple of pi....

 

Here ...cos(cosx) let it be as ...cos(y)   and y as cosx ..

 

Now ...y will have its value lying between [-1,1]  Since zero falls in this range ..hence cos(y) or cos(cosx) has maximum value equal to 1  ...i.e  a = 1

 

But pi doesn't fall in the range of [-1,1] ...so cos(cosx) will never be minimum at pi or it equivalent..it will have a different minimum value ..

 

Now cosx is a decreasing function ..so if u put x as minimum it will give maximum and if u put it as maximum it will give minimum .. Out concern here is to get minimum value ..

 

So minimum value of  cos(y)  is when y(=cosx)=1 ...i.e b = cos1

 

SO b = cos a 

 

The only way to do such questions in a good and faster approach is practice...solve as much question as u can..u will get confident and feeling that u r approaching fastly and doing good in trignometry ..

 

Wishes...

 

Regards

 

Yagya

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