Exact Form:
t=1+√61/6,1−√61/6
t=1+61/6,1-61/6
Decimal Form:t=1.46837494…,−1.13504161
Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
![(a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x](https://tex.z-dn.net/?f=%28a%29%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D%5Csin%20%5E2x%2B%5Ccos%20%5E2x%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B%5Csin%202x)

![(c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x](https://tex.z-dn.net/?f=%28c%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x%7D%7B%5Csin%20x%5Ccos%20x%7D%3D%5Cdfrac%7B3%5Csin%20x-4%5Csin%20%5E3x%7D%7B%5Csin%20x%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%203%5Csec%20x-4%5Csin%20%5E2x%5Csec%20x%5C%5C%5CRightarrow%203%5Csec%20x-4%5B1-%5Ccos%20%5E2x%5D%5Csec%20x%5C%5C%5CRightarrow%20%203%5Csec%20x-4%5Csec%20x%2B4%5Ccos%20x%5C%5C%5CRightarrow%204%5Ccos%20x-%5Csec%20x)
![(d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x](https://tex.z-dn.net/?f=%28d%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x-%5Csin%20x%7D%7B%5Ccos%203x%2B%5Ccos%20x%7D%3D%5Cdfrac%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%20%5Csin%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%5Ccos%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2%5Ccos%202x%5Csin%20x%7D%7B2%5Ccos%202x%5Ccos%20x%7D%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%20%5Ctan%20x)
Thus, all the identities are correct.
Answer:
56a + 40b
Step-by-step explanation:
hope this helps!
Answer:
2nd
Step-by-step explanation:
The blocks from the bottom up are: 123. Each column has one 1 one 2 and one 3. So only 2 can be the right answer.
I'm not that familiar with these problems, check my answer just in case.
T(1÷3)=2
t=2÷(1÷3)
t=2×3
t=6