Question

Provide some useful trigonometric identities.
At least 10.
:)

Answer 1

1) sin²x + cos²x = 1

2) sec²x - tan²x = 1

3) cosec²x - cot²x = 1

4) tanx = sinx/cosx

5) cotx = cosx/sinx

6) sin ( A+B ) = sinA cosB + cosA sinB

7) sin ( A-B ) = sinA cosB - cosA sinB

8) cos ( A+B ) = cosA cosB - sinA sinB

9) cos ( A-B ) = cosA cosB + sinA sinB

10) tan ( A+B ) = tanA + tanB / 1 - tanA tanB

11) tan ( A-B ) = tanA + tanB / 1 + tanA tanB

12) cot ( A+B ) = cotB cotA - 1 / cotB + cotA

13) cot ( A-B) = cotB cotA + 1 / cotB - cotA

14) sin ( A+B ). sin ( A-B) = sin²A - sin²B

= cos²B - cos²A

15) cos ( A+B ). cos ( A-B ) = cos²A - sin²B

= cos²B - sin²A

16) sin2A = 2 sinA cosA

17) cos2A = cos²A - sin²A

18) tan2A = 2tanA / 1 - tan²A

19) cot2A = cot²A - 1 / 2cotA

20) sin3A = 3sinA - 4sin³A

21) cos3A = 4cos³A - 3cosA

22) tan3A = 3tanA - tan³A / 1 - 3tan²A

23) sin ( A+B ) + sin ( A-B ) = 2 sinA cosB

24) sin ( A+B ) - sin ( A-B ) = 2 cosA sinB

25) cos ( A+B ) + cos ( A-B ) = 2 cosA cosB

26) cos ( A+B ) - cos ( A-B ) = -2 sinA sinB

HOPE U UNDERSTAND

PLS MARK IT AS BRAINLIEST

Answer 2

★ sin∅ = P/h , cos∅ =b/h, tan∅ =P/b

★ sin∅ = 1/cosec∅,
cos∅ = 1/sec∅
tan∅ = 1/cot∅

★ sin∅, cosec∅→ positive in 1st and 2nd quadrant
cos∅, sec∅→ positive in 1st and 4th quadrant
tan∅, cot∅→positive in 1st and 3rd quadrant

★ sin²∅ + cos²∅ = 1,
sec²∅ -tan²∅ = 1
cosec²∅ - cot²∅ = 1

★ sin( A + B) = sinA.cosB + cosA.sinB
sin(A-B) = sinAcosB - cosA.sinB
cos(A +B) = cosA.cosB-sinA.sinB
cos(A-B) = cosA.cosB-sinA.sinB
tan( A +B) = ( tanA+ tanB)/(1-tanA.tanB)
tan(A-B) =(tanA-tanB)/(1+tanA.tanB)

★ -1 ≤ sin∅ ≤ 1 ,
-1 ≤ cos∅ ≤ 1
tan∅ €R { € belongs to
cot∅ € R
sec∅€R -( -1 , 1) { except -1 to 1
cosec∅€R-( -1 , 1)

★ asin∅ + bcos∅ = C
then, maximum value of C = √(a² + b²)
minimum value of C = -√(a² + b²)

★ sin²x + cosec²x ≥ 2
cos²x + sec²x ≥ 2
tan²x + cot²x ≥ 2

★tan∅ = cot∅ -2cot2∅
tan3∅ = tan∅.tan(60-∅).tan(60+∅)
sin3∅ =4sin∅.sin(60-∅).sin(60+∅)
cos3∅=4cos∅.cos(60-∅).cos(60+∅)

★ 2 sin²∅ = ( 1-cos2∅)
2cos²∅ =(1 +cos2∅)