If sec A = 13/5 then length
of perpendicular is equal to
Answers
Answer:
Given: ..... (a)
To prove: .
We know that the trigonometric ratio:
Substituting the value from equation (a), we get
…… (b)
Also,
…… (c)
Comparing equation (b) and equation (c), we get
, BC = 5 and Hypotenuse, AC = 13
Applying Pythagoras theorem in ΔABC to get the length of perpendicular AB, we get
…… (d)
Thus, the length of the Perpendicular, AB = 12.
We know that the trigonometric ratio:
Substituting the value of known sides, we get
…… (e)
Now, solving the L.H.S. of the equation , we get
Substituting the values of and from equation (b) and equation (e) respectively, we get
Therefore, L.H.S. = R.H.S.
Hence, it is proved that .
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Exercise 10.1 Questions
Q. 1
In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. (i) sin A = 2 3 (ii) cos A = 4 5 (iii) tan θ = 11 (iv) sin θ = 11 15 (v) tan α = 5 12 (vi) sin θ = 3 2 (vii) cos θ = 7 25 (viii) tan θ = 8 15 (ix) cot θ = 12 5 (x) sec θ = 13 5 (xi) cosec θ = 10 (xii) cos θ = 12 15 ...
Q. 2
In a ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine (i) sin A, cos A ...
Q. 3
In Fig. 5.37, find tan P and cot R. Is tan P = cot R? Figure ...
Q. 4
If sin A = 9 41 , compute cos A and tan A . ...
Q. 5
Given 15 cot A = 8, find sin A and sec A . ...
Q. 6
In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R. ...
Q. 7
If cot θ = 7 8 , evaluate : (i) 1 + sin θ 1 - sin θ 1 + cos θ 1 - cos θ (ii) cot 2 θ ...
Q. 8
If 3 cot A = 4, check whether 1 - tan 2 A 1 + tan 2 A = cos 2 A - sin 2 A or not. ...
Q. 9
If tan θ = a b , find the value of cos θ + sin θ cos θ - sin θ . ...
Q. 10
If 3 tan θ = 4, find the value of 4 cos θ - sin θ 2 cos θ + sin θ . ...
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If sec A = 13/5 then length
of perpendicular is equal to