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Question

Find sin x2, cos x2 and tan x2 in each of the following: 

tan x = - 43, x in quadrant II. 


Solution

Here tan x = 43, x in quardrant II 

sec2 x = 1 + tan2 x

sec2 x =1 + (43)2=1+169=259

sec x = ±53 cos x = ±35

But x lies in the second quadrant. 

cos x = 35  

Also π2<x<ππ4<x2<π2

So x2, cos x2 and tan x2 are all positive. 

Now, cos x2=1+cos x2=1352

= 15×55=55

sin x2=1cos x2=1+352

= 45=25×55=255

tan x2=sinx2cosx2=2515 = 2.


Mathematics

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