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Can someone help me prove this trig ID?
cot^2a=cos^2a+(cota*cosa)^2
^2= squared
2 Answers
- Anonymous9 years agoFavorite Answer
notice Cot(a) is both 1/tan and cos/sin.
Cot(a)^2=cos(a)^2+((cos(a)/sin(a) * cos(a))^2
cos(a)^2/sin(a)^2=cos(a)^2 + (cos(a)^4/sin^2(a))
cos(a)^2 = cos(a)^2 * sin(a)^2 + cos(a)^4
cos(a)^2 - cos(a)^4 = cos(a)^2 * sin(a)^2
cos(a)^2 (1-cos(a)^2) = cos(a)^2 * sin(a)^2
Notice 1 - cos(a)^2 = sin(a)^2 ------>Trig identity.
By dividing by cos(a)^2 and using the previously stated trig identity we have
sin(a)^2 = sin(a)^2
Proven ;)
Hope i helped.
Source(s): Math Major - ComoLv 79 years ago
Let us refer to angle as Ө for no other reason that it looks better !
RHS
cos²Ө + ( cos Ө cos Ө / sin Ө )²
cos²Ө + ( cos²Ө / sin Ө )²
cos²Ө + (cosӨ)^4 / sin²Ө
cos²Ө sin²Ө + (cosӨ)^4
------------------------------------
sin²Ө
cos²Ө [ sin²Ө + cos²Ө ]
-----------------------------------
sin²Ө
cos²Ө
----------
sin²Ө
cot²Ө
RHS
---------
cot²Ө
LHS = RHS