M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 17 trigonometric identities

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 26^o + cos 64^o sin 26^o + (tan 36^o/ cot 54^o)

(sec 17^o/ cosec 73^o) + (tan 68^o/ cot 22^o) + cos² 44^o + cos² 46^o

(sin 65^o/ cos 25^o) + (cos 32^o/sin 58^o) – sin 28^o sec 62^o + cosec² 30^o

(sin 29^o/ cosec 61^o) + 2 cot 8° cot 17° cot 45° cot 73° cot 82° – 3(sin² 38° + sin² 52°).

(sin 35^o cos 55^o + cos 35^o sin 55 ^o)/ (cosec² 10^o – tan² 80 ^o)

sin² 34^o + sin² 56^o + 2 tan18^o tan 72^o – cot² 30^o

(tan 25^o/ cosec 65^o)² + (cot 25^o/ sec 65^o)² + 2 tan 18^o tan 45^o tan 75^o

(cos² 25^o + cos² 65^o) + cosec θ sec (90^o – θ) – cot θ tan (90^o – θ)

Prove that following:

cos θ sin (90° – θ) + sin θ cos (90° – θ) = 1

Prove that following:

tan θ/ tan (90^o – θ) + sin (90^o – θ)/ cos θ = sec² θ

Prove that following:

(cos (90^o – θ) cos θ)/ tan θ + cos² (90^o – θ) = 1

Prove that following:

sin (90^o – θ) cos (90^o – 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