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1oth maths solutions

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Mathematics
(www.tiwariacademy.net)
(Class X)
www.tiwariacademy.com A Free web support in education
1
Question 1:
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Answer 1:
We know that,
Question 2:
Write all the other trigonometric ratios of
∠
A in terms of sec A.
Answer 2:
We know that, Therefore, We know that, However, Therefore, Also,
Mathematics
(www.tiwariacademy.net)
(Class X)
www.tiwariacademy.com A Free web support in education
2 Also, sin
2
A + cos
2
A = 1 sin
2
A = 1 − cos
2
A tan
2
A + 1 = sec
2
A tan
2
A = sec
2
A − 1
Question 3:
Evaluate (i)
(ii)
sin25° cos65° + cos25° sin65°
Answer 3:
(i)
Mathematics
(www.tiwariacademy.net)
(Class X)
www.tiwariacademy.com A Free web support in education
3 = 1 (ii) sin25° cos65° + cos25° sin65° = sin
2
25° + cos
2
25° = 1 (As sin
2
A + cos
2
A = 1)
Question 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) (A)
sec
2
A (B)
−
1 (C) cot
2
A (D) tan
2
A
Answer 4:
(i) 9 sec
2
A − 9 tan
2
A = 9 (sec
2
A − tan
2
A) = 9 (1) [As sec
2
A − tan
2
A = 1] = 9 Hence, alternative (B) is correct.
Mathematics
(www.tiwariacademy.net)
(Class X)
www.tiwariacademy.com A Free web support in education
4
(ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ)
Hence, alternative (C) is correct. (iii)
(secA + tanA) (1 − sinA)
= cosA Hence, alternative (D) is correct. (iv)
Hence, alternative (D) is correct.

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