Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

For all x in [0,90] show that cos(sinx)>sin(cosx) I understood the solution given in my book which said Cosx +sinx Cosx But if Sinx Then when we take sin and cos both sides resp we get two different opposite answers. Please explain to me where I have gone wrong.

For all x in [0,90] show that cos(sinx)>sin(cosx)
I understood the solution given in my book which said 
Cosx +sinx
Cosx
But if 
Sinx
Then when we take sin and cos both sides resp we get two different opposite answers.
Please explain to me where I have gone wrong.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I am assuming 90 to be pi/2.

For
x\in [0, \frac{\pi }{2}]
0\leq sinx\leq 1
0\leq cosx\leq 1
f_{1}(x) = cos(sinx)
sinx will take value from 0 to 1 in increasing order.
cos(sin1)\leq f_{1}(x)\leq 1
f_{2}(x) = sin(cosx)
cosx will take value from 1 to 0.
0\leq f_{2}(x)\leq sin(cos1)
If you can draw the graph, it will be more clear.


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free