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If a sec x – c tan x = d and b sec x + d tan x = c , then prove that a² + b² = c² + d²

If a sec x – c tan x = d and b sec x + d tan x = c , then prove that a² + b² = c² + d²

Grade:10

1 Answers

Chirag jain
16 Points
5 years ago
aSecx-ctanx=d
So, a=(d+ctanx) /secx____1
bSecx+dtanx=c
So, b=(c-dtanx) /secx_____2
Now, squaring eq. 1&eq.2
So,a^2+b^2=(d^2+c^2tan^2x+2cdtanx+c^2+d^2tan^2x-2cdtanx)/sex^2x
a^2+b^2=(d^2+c^2tan^2x+c^2+d^2tan^2x)/sec^2x
a^2+b^2=[d^2(1+tan^2x)+c^2(1+tan^2x)]/sec^2x
a^2+b^2=[(1+tan^2x)(c^2+d^2)]/sec^2x
a^2+b^2=[sec^2x(c^2+d^2)]/sec^2x
So,a^2+b^2=c^2+d^2
                     HENCE PROVED
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