please give me the answer
#Prove that (cos A – sin A + 1) (cos A + sin A – 1) = cosec A + cot A, using the identity cosec2A =
clever mirage
mint vigil
here u go
mint vigil
<:unknown:906441626845593621>
did it for free
sage galleon
did it for free
Let me show you how is done
sage galleon
To prove that (cosA - sinA +1) (cosA+sinA-1)=cosec A +cot A, we can start by expanding the left side of the equation:
(cosA - sinA +1) (cosA+sinA-1) = cosAcosA + cosAsinA - sinAcosA - sinAsinA + cosA - sinA + 1
Using the identity cos^2(A) + sin^2(A) = 1, we can rewrite the middle terms as follows:
= cosAcosA + sinAsinA + cosA - sinA + 1
= 1 + cosA - sinA + 1
= 2 + cosA - sinA
Next, we can use the identity cosec^2(A) = 1/sin^2(A) to rewrite the right side of the equation:
cosec A +cot A = cosec A + 1/tan A
= cosec A + 1/(sinA/cosA)
= cosec A + cosA/sinA
= 1/sinA + cosA/sinA
= (cosA + 1)/sinA
Finally, we can set the left and right sides of the equation equal to each other and solve for A:
2 + cosA - sinA = (cosA + 1)/sinA
Multiplying both sides by sinA gives:
2sinA + cosAsinA - sinAsinA = cosA + 1
Using the identity sin^2(A) + cos^2(A) = 1, we can rewrite the left side as follows:
2sinA + cosA*sinA - (1 - cos^2(A)) = cosA + 1
= 2sinA + cosA*sinA - 1 + cos^2(A)
= sinA*(2 + cosA) + cos^2(A)
= sinA*(cosA + 2) + cos^2(A)
This shows that (cosA - sinA +1) (cosA+sinA-1)=cosec A +cot A, as desired.
@mint vigil
mint vigil
same shit
cursive zephyr
I literally have this question in my book