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Activity : Construct a table of the following trig onometric formulae for easy memorizing. θ θ sin 1 cosec θ θ cos 1 sec θ θ c ...

Solution : Given that, tanA 1. So, opposite side of the A = 1, adjacent side = 1 hypotenuse = 12  12 2 Therefore, sinA= 2 1 , c ...

= θ θ 2 2 1 sin 1 sin   = 1 = R.H.S. (proved) Example 6. Prove that : 1 2 n 1 2 n 1 si^2 A ta^2 A^ Proof : L.H.S. = si^2 A ...

Prove : L.H.S. = siA siA 1 n 1 n   = ( 1 n )( 1 n ) ( 1 n )( 1 n ) siA siA siA siA     = si A siA 2 2 1 n ( 1 n )   = co ...

or, sec^2 Atan^2 A 1 or, (secAtanA)(secAtanA) 1 or, ( c n ) 1 2 5 seAtaA [from (i)] ∴ 5 2 secAtanA Exercise 9⋅ 1 Verify wh ...

0DWK,;;)RUPD θ θ θ θ 1 sin 1 sin (tan sec )^2    18. cotA.tanB. cotB tanA cotA tanB   secA tanA. 1 sinA 1 sinA  ...

 3 1 3 tan 30 a a OM $ PM . 2 2 cosec 30 a a PM $ OP , 3 2 3 2 sec 30 a a OM $ OP 3 3 cot 30 a a PM $ OM . Similarly, 2 3 2 3 s ...

Trigonometric ratios of complementary angles Let, ‘XOY θ and P is the point on the side OY of the angle. We drawPMAOX. Since the ...

When the angle θ comes closer to 0 $, the length of the line segment PN reduces to zero and in this case the value of OP PN sinθ ...

angle Ratio 0 $ 30 $ 45 $ 60 $ 90 $ sine 0 2 1 2 1 2 3 1 cosine 1 2 3 2 1 2 (^10) tangent 0 3 (^113) undefined cotangent undefin ...

Solution : (a) Given expression = $ $ $ n 45 1 n 45 1 n (^452) 2 2 ta si si    = () [ I n 45 1 ] 2 1 1 n 45 2 1 1 2 1 1 2 2 2 ...

(b) If 1 3 1 3 cosA sinA cosA sinA     , find the value of A. (c) Prove that, 1 tanA 1 tanA cos 2 A 2 2   , if A 45 $. (d) ...

or, 2 3 2 2 n 2 s   siA coA or, 3 1 n s siA coA or, cotA cot 60 $ ? A 60 $ (c) Given that, A 45 $ we have to prove that, ta A ...

0DWK,;;)RUPD (i)sin^2 θ 1 cos^2 θ (ii)sec^2 θ 1 tan^2 θ (iii)cot^2 θ 1 tan^2 θ Which one of the followings is correct ...

If cos(AB) 1 , 2 sin(AB) and A,B are acute angle, find the values of AandB. Solve : 3 1 3 1 cosA sinA cosA sinA     . I ...

Chapter Ten Distance and Height From very ancient times trigonometrical ratios are applied to find the distance and height of an ...

Activity : Point the figure and show the horizontal line, vertical line, vertical plane, angle of elevation and angle of depress ...

BC AB tan‘ACB or, >@n 60 3 105 n 600 ta^0 x ta  or, x 105 3 or, 3 x 105 or, 3 105 x or, 3 105 3 x or, x 35 3 ?x 60. 622 (app ...

Solution : Let, the height of the stick from the foot learned against the tree of AB 7 metre and angle of depression is ‘DBC 30 ...

or, 3 h h 42 3 or, 3 hh 42 3 or, 3  1 h 42 3 or, 3 1 42 3  h ?h 99. 373 (app.) `Height of the building is 99. 373 metres ( ...