Please Help!!!
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
=cot x (sec²x)²
=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]
= cot x(1+ 2 tan²x +tan⁴x)
=cot x+ 2 cot x tan²x+cot x tan⁴x
=cot x +2 tan x + tan³x [ ∵cot x tan x =1]
=R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
L.H.S =(sin x)(tan x cos x - cot x cos x)
= sin x tan x cos x - sin x cot x cos x
= sin²x -cos²x
=1-cos²x-cos²x
=1-2 cos²x
=R.H.S
3.
1+ sec²x sin²x =sec²x
L.H.S =1+ sec²x sin²x
= [
]
=1+tan²x
=sec²x
=R.H.S
4.
L.H.S=
= 2 csc x
= R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
= sec²x-tan²x
=
=1
The bases are both 2, so we would subtract the exponents. This is because the rule is
(a^b)/(a^c) = a^(b-c)
In this case,
a = 2
b = 3/4
c = 1/2
So this means
b - c = (3/4) - (1/2) = (3/4) - (2/4) = 1/4
After subtracting the exponents, the final exponent is 1/4
So the expression simplifies to 2^(1/4) which is the same as![\sqrt[4]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D)
(fourth root of 2)
(a^b)/(a^c) = a^(b-c)
In this case,
a = 2
b = 3/4
c = 1/2
So this means
b - c = (3/4) - (1/2) = (3/4) - (2/4) = 1/4
After subtracting the exponents, the final exponent is 1/4
So the expression simplifies to 2^(1/4) which is the same as