# Introduction to Trigonometry – Exercise 8.4 – Class 10

1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. Solution:

We know that, 2. Write all the other trigonometric ratios of ∠A in terms of sec A.

Solution:

We know that 3. Evaluate (i) (sin263° + sin227°)/(cos217°+cos273°)

(ii) sin25° cos65° + cos25° sin65°

Solution:

(i)  (ii)sin25° cos65° + cos25° sin65°

= (sin25°){cos(90°-25°)} + cos25°{sin(90°-25°)}

= (sin25°)(sin25°)+(cos25°)(cos25°)

= (sin225°) + cos225°

= 1

4. Choose the correct option. Justify your choice.

(i) 9 sec2A − 9 tan2 A =

(A) 1

(B) 9

(C) 8

(D) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ)

(A) 0

(B)1

(C) 2

(D) −1

(iii) (secA + tanA) (1 − sinA) =

(A) secA

(B) sinA

(C) cosecA

(D) cosA

(iv)(1+tan2A)/(1+cot2A) =

(A) sec2A

(B) -1

(d) tan2A

Solution:

(i) 9 sec2 A − 9 tan2 A

= 9 (sec2 A – tan2 A)

= 9 (1)  [Because  sec2 A − tan2 A = 1]

= 9

(B) is correct.

(ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ) (C) is correct.

(iii) = cosA

(D) is correct.

(iv) (D) is correct.

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined. Solution:  Solution: (iii) Solution: = secθ cosec θ + 1 = R.H.S.

(iv) Solution: (v) solution: = cosec A + cot A = R.H.S

(vi) Solution: ## 9 thoughts on “Introduction to Trigonometry – Exercise 8.4 – Class 10”

1. Lady G says:

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1. breathmath says:

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2. Cradle of Joy says:

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1. breathmath says:

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1. Cradle of Joy says:

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2. breathmath says:

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2. breathmath says:

If you want more clarification, you are always welcome

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3. breathmath says:

Powers or exponents are easy to write in word document ,from there we can copy and paste in WordPress

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