If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigonometric identities).
If A is an acute angle and sec A = 17/8, find all other trigonometric ratios of angle A (using trigonometric identities).
Express the ratios cos A, tan A and sec A in terms of sin A.
cos2 26o + cos 64o sin 26o + (tan 36o/ cot 54o)
(sec 17o/ cosec 73o) + (tan 68o/ cot 22o) + cos2 44o + cos2 46o
(sin 65o/ cos 25o) + (cos 32o/sin 58o) – sin 28o sec 62o + cosec2 30o
(sin 29o/ cosec 61o) + 2 cot 8° cot 17° cot 45° cot 73° cot 82° – 3(sin² 38° + sin² 52°).
(sin 35o cos 55o + cos 35o sin 55 o)/ (cosec2 10o – tan2 80 o)
sin2 34o + sin2 56o + 2 tan18o tan 72o – cot2 30o
(tan 25o/ cosec 65o)2 + (cot 25o/ sec 65o)2 + 2 tan 18o tan 45o tan 75o
(cos2 25o + cos2 65o) + cosec θ sec (90o – θ) – cot θ tan (90o – θ)
Prove that following:
cos θ sin (90° – θ) + sin θ cos (90° – θ) = 1
tan θ/ tan (90o – θ) + sin (90o – θ)/ cos θ = sec2 θ
(cos (90o – θ) cos θ)/ tan θ + cos2 (90o – θ) = 1
sin (90o – θ) cos (90o – θ) = tan θ/ (1 + tan2 θ)
tan A + cot A = sec A cosec A
sin A/ (1 + cos A) = (1 – cos A)/ sin A
(sec A – 1)/(sec A + 1) = (1 – cos A)/(1 + cos A)
sec2 A + cosec2 A = sec2 A. cosec2 A
(1 + sin A)/ cos A + cos A/ (1 + sin A) = 2 sec A
cosec A/ (cosec A – 1) + cosec A/ (cosec A + 1) = 2 sec2 A
cot A – tan A = (2cos2 A – 1)/ (sin A – cos A)
(cot A – 1)/ (2 – sec2 A) = cot A/ (1 + tan A)
tan2 θ – sin2 θ = tan2 θ sin2 θ
cosec4 θ – cosec2 θ = cot4 θ + cot2 θ
2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ.
cos A cot A/ (1 – sin A) = 1 + cosec A
sec4 A – tan4 A = 1 + 2 tan2 A
\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\cot ^{2} A}{1+\cot ^{2} A}=1
(tan A + sin A)/ (tan A – sin A) = (sec A + 1)/ (sec A – 1)
If 7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.
If sec θ + tan θ = m and sec θ – tan θ = n, prove that mn = 1.
If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.
\sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{\sin A}{1+\cos A}
If sin θ + cos θ = √2 sin (90° – θ), show that cot θ = √2 + 1
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