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..

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

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