**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) **(sin^{2}63° + sin^{2}27°)/(cos^{2}17°+cos^{2}73°)

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

Solution:

(i)

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

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

= (sin25°)(sin25°)+(cos25°)(cos25°)

= (sin^{2}25°) + cos^{2}25°

= 1

**4. Choose the correct option. Justify your choice. **

**(i) 9 sec ^{2}A − 9 tan^{2} 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+tan ^{2}A)/(1+cot^{2}A) = **

**(A) sec ^{2}A**

**(B) -1**

**© cot ^{2}A**

**(d) tan ^{2}A**

Solution:

(i) 9 sec^{2} A − 9 tan^{2} A

= 9 (sec^{2} A – tan^{2} 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 responses to “Introduction to Trigonometry – Exercise 8.4 – Class 10”

[…] Introduction to Trigonometry – Exercise 8.4 […]

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Oh how I wish I understood this. I have always admired people who excel in Mathematics; therefore, I admire you!

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Haha! Thank you so much

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Very nice post! I have seen first in WordPress. Can you please tell me how you write mathematical numbers in your blog because its difficult to show powers or exponents what app you used. Can you please tell me.

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Yeah sure… we have many mathematical symbol in WordPress itself . Very few like fractions that we need to do write in HTML page and other symbols like cube root, 4th root, nth root etc are easy to write in word document ,then we need to copy it to WordPress

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Thanks! You solved my confusion. Your posts are very nice, keep it up!

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That’s my pleasure!

Thanks for visiting my site, keep peeping here

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If you want more clarification, you are always welcome

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

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