ত্রিকোণমিতির সকল সূত্র

 ত্রিকোণমিতি শব্দটি এসেছে গ্রীক শব্দ trigonon ("ত্রিভুজ") এবং মেট্রন ("পরিমাপ করতে")

sinθ=लম্ব/অতিভূজ	cotθ=ভূমি/লম্ব
cosθ=ভূমি/অতিভূজ	secθ=অতিভূজ/ভূমি
taneθ=लম্ব/ভূমি	cosecθ=অতিভূজ/লম্ব

cosec θ = 1/sin θ	sinθ=1/cosecθ
sec θ = 1/cos θ	cosecθ=1/sinθ
cot θ = 1/tan θ	cosθ=1/secθ
sin θ = 1/cosec θ	secθ=1/cosθ
cos θ = 1/sec θ	tanθ=1/cotθ
tan θ = 1/cot θ	cotθ=1/tanθ

 

sin²θ + cos²θ= 1	sec²θ = 1+ tan²θ
sin²θ = 1 – cos²θ	tan²θ = sec²θ – 1
cos²θ = 1- sin²θ	cosec²θ – cot²θ = 1
sec²θ – tan²θ = 1	cosec²θ = cot²θ + 1
cot²θ = cosec²θ – 1

sin (A + B) = sin A cos B + cos A sin B	sin (A − B) = sin A cos B – cos A sin B
cos (A + B) = cos A cos B – sin A sin B	cos (A – B) = cos A cos B + sin A sin B
tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]	tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

    

sin2A = 2sinA . cosA                 = [2tan A/(1+tan2 A)]  cos2A = cos2A–sin2A                  = [(1-tan2 A) / (1+tan2 A)] cos2A = 2cos2A−1                  = 1–2sin2A

1. tan(2x) = [2tan(x)]/ [1−tan2(x)]
2. sec (2x) = sec2 x/(2-sec2 x)
3. cos (2x) = (sec x. cos x)/2
4. Sin 3x = 3sin x – 4sin3x
5. Cos 3x = 4cos3x-3cos x
6. Tan 3x = [3tanx-tan3x]/[1-3tan2x]
7. sin x sin y = 1/2 [cos(x–y) − cos(x+y)]
8. cos x cos y = 1/2[cos(x–y) + cos(x+y)]
9. sin x cos y = 1/2[sin(x+y) + sin(x−y)]
10. cos x sin y = 1/2[sin(x+y) – sin(x−y)]
11. sin C + sin D = 2 sin [(C+D)/2] cos [(C-D)/2]
12. sin C – sin D = 2 cos [(C+D)/2] sin [(C-D)/2]
13. cos C + cos D = 2 cos [(C+D)/2] cos [(C-D)/2]
14. cos C – cos D = -2 sin [(C+D)/2] sin [(C-D)/2]