SOLUTION: 1.i need to verify the identity of sin^2x+sin^2xcot^2x=1 2. verify the identity of cscx(sinx+cosx)=1+cotx 3. Verify the identity of (sinx+cosx)^2/1+2sinxcosx =1 4. verify

Algebra ->  Trigonometry-basics -> SOLUTION: 1.i need to verify the identity of sin^2x+sin^2xcot^2x=1 2. verify the identity of cscx(sinx+cosx)=1+cotx 3. Verify the identity of (sinx+cosx)^2/1+2sinxcosx =1 4. verify       Log On


   

Question 947103: 1.i need to verify the identity of sin^2x+sin^2xcot^2x=1
2. verify the identity of cscx(sinx+cosx)=1+cotx
3. Verify the identity of (sinx+cosx)^2/1+2sinxcosx =1
4. verify the identity cos^2x-sin^2x/1-tan^2x=cos^2x
5. verifty the identity 2tanx-(1+tanx)^2=-sec^2x

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
sin%5E2%28x%29%2Bsin%5E2%28x%29cot%5E2%28x%29=1+
sin%5E2%28x%29%281%2Bcot%5E2%28x%29%29=1 ...................use 1%2Bcot%5E2%28x%29=csc%5E2%28x%29
sin%5E2%28x%29+csc%5E2%28x%29=1...............use csc%5E2%28x%29=1%2Fsin%5E2%28x%29
sin%5E2%28x%29+%2Fsin%5E2%28x%29=1
1=1

2.
csc%28x%29%28sin%28x%29%2Bcos%28x%29%29=1%2Bcot%28x+%29 .................use csc%28x%29=1%2Fsin%28x%29
%281%2Fsin%28x%29%29%28sin%28x%29%2Bcos%28x%29%29=1%2Bcot%28x+%29+
sin%28x%29%2Fsin%28x%29%2Bcos%28x%29%2Fsin%28x%29=1%2Bcot%28x+%29+
1%2Bcot%28x+%29=1%2Bcot%28x+%29+

3.
%28sin%28x%29%2Bcos%28x%29%29%5E2%2F%281%2B2sin%28x%29cos%28x%29%29+=1+
...........use sin%5E2%28x%29%2Bcos%5E2%28x%29=1
%281%2B2sin%28x%29cos%28x%29%29%2F%281%2B2sin%28x%29cos%28x%29%29+=1
1+=1

4.
%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%281-tan%5E2%28x%29%29=cos%5E2%28x+%29
%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%281-tan%5E2%28x%29%29=cos%5E2%28x+%29
%28cos%5E2%28x%29-sin%5E2%28x%29%29=cos%5E2%28x+%29 ..........tan%5E2%28x%29=sin%5E2%28x%29%2Fcos%5E2%28x+%29








cos%5E2%28x+%29=cos%5E2%28x+%29

5.
2tan%28x%29-%281%2Btan%28x%29%29%5E2=-sec%5E2%28x%29
2tan%28x%29-%281%2B2tan%28x%29%2Btan%5E2%28x%29%29=-sec%5E2%28x%29
cross%282tan%28x%29%29-1-cross%282tan%28x%29%29-tan%5E2%28x%29=-sec%5E2%28x%29
-1-tan%5E2%28x%29=-sec%5E2%28x%29
-%281%2Btan%5E2%28x%29%29=-sec%5E2%28x%29..............1%2Btan%5E2%28x%29=sec%5E2%28x%29
-%28sec%5E2%28x%29%29=-sec%5E2%28x%29
-sec%5E2%28x%29=-sec%5E2%28x%29