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Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Write all the other trigonometric ratios of in terms of sec A.
We know that,
Also, sin2 A + cos2 A = 1
sin2 A = 1 − cos2 A
tan2A + 1 = sec2A
tan2A = sec2A − 1
Evaluate:
(i)
(ii)
(i)
sinx= cos(90-x)
sin 63 = cos(90-63) =cos 27
sin 27 = cos(90-27) =cos 63
sin 17 = cos(90-17) =cos 73
sin 73 = cos(90-73)=cos 17
=
= 1
=
= 1
By using the fact that
Hence, answer is 1
(ii)
sin 25 = cos(90-25) = cos 65
cos 25 = sin(90-25) = sin 65
Hence, cos25 sin65 + cos65 sin25 = cos25 x cos25 + sin25 x sin25 =1
Bu using the fact that
Choose the correct option. Justify your choice.
(i)
(A) 1 (B) 9 (C) 8 (D) 0
(ii)
(A) 0 (B) 1 (C) 2 (D) –1
(iii)(sec A + tan A) (1 – sin A) =
(A) sec A (B) sin A (C) cosec A (D) cos A
(iv)
(A) (B)
(C)
(D)
(i) 9 sec2A − 9 tan2A
= 9 (sec2A − tan2A)
= 9 (1) [As sec2 A − tan2 A = 1]
= 9
Hence, alternative (B) is correct.
(ii)
(1 + tan θ + sec θ) (1 + cot θ − cosec θ)
Hence,option (C) is correct.
(iii) (secA + tanA) (1 − sinA)
=
= cosA
Hence, option (D) is correct.
(iv)
Hence, option (D) is correct.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(i)
(ii)
(iii)
[Hint : Write the expression in terms of and
]
(iv)
[Hint :Simplify LHS and RHS separately]
(v) , using the identity
(vi)
(vii)
(viii)
(ix)
[Hint: Simplify LHS and RHS separately]
(x)
(i) 
(ii) 
(iii) 
= secθ cosec θ +
= R.H.S.
(iv) 
= R.H.S
(v) 
Using the identity cosec2
= 1 + cot2,
L.H.S = 
= cosec A + cot A
= R.H.S
(vi) 
(vii) 
(viii) 
(ix) 
Hence, L.H.S = R.H.S
(x) 
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