Question

If cot theta 7 by 8 evaluate

Answer 1

Ex 8.1, 7 If cot θ = 7/8 , evaluate : (i) ((1 + ⁡)(1 − ⁡))/((1 + ⁡)(1 − ⁡)) We will first calculate the value of sin θ & cos θ Now, tan θ = 1/cot⁡ tan θ = 1/(7/8) tan θ = 8/7 ( ∠)/( ∠)=8/7 /=8/7 Let BC = 8x & AB = 7x We find AC using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 AC2 = AB2 + BC2 AC2 = (7x)2 + (8x)2 AC2 = 49x2 + 64x2 AC2 = 113x2 AC = √1132 AC = √113 x Now, we need to find sin θ and cos θ sin = ( ∠)/ = / = 8/(√113 ) = 8/(√113 ) Here, We have to evaluate ((1 + sin⁡ ) (1 −〖 sin〗⁡ ))/((1 + cos⁡ ) (1 −〖 cos〗⁡ ) ) Using (a + b) (a – b) = a2 – b2 = ( (12 − 2 ))/( (12 − 2)) = ( (1 − 2 ))/( (1 − 2)) Putting sin = 8/(√113 ) & cos θ = 7/(√113 ) = ((1 − (8/(√113 ))^2 ))/((1 − (7/(√113 ))^2 ) ) = ((1 − 8^2/(√113)2))/((1 − 72/(√113)2) ) = ((1 − 64/113))/((1 − 49/113) ) = (((113 − 64)/113))/(((113 − 49)/113) ) = (113 − 64)/(113 − 49 ) = 49/(64 ) Hence, ((1 + ⁡)(1 − ⁡))/((1 + ⁡)(1 − ⁡)) = 49/(64 )


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