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

Exercises in Chapter 17 trigonometric identities Grade 10

Trigonometric Identities Exercise 18

Questions in Trigonometric Identities Exercise 18

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

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Chapters in this book

GST

Banking

Shares and Dividends

Quadratic Equations in One Variable

Factorization

Ratio and Proportion

Matrices

Arithmetic and Geometric Progression

Reflection

Section Formula

Equation of Straight Line

Similarity

Locus

Circles

Constructions

Mensuration

Trigonometric Identities

Trigonometric Tables

Heights and Distances