Trigonometry> if tan theta +sec theta = x then show tha...

if tan theta +sec theta = x then show that sin theta = x2 - 1+x2 + 1

Naveen Arun Kumar Nair , 8 Years ago

Grade 10

2 Answers

Ajay

Last Activity: 8 Years ago

the question is wrong

In this casxe sin theta = x^2/(1+x^2). and not what you have mentioned’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’

Aman Pandey

Last Activity: 7 Years ago

We know that (sec theta + tan theta) (sec theta - tan theta)=1Now, Sec theta + tan theta =1 (given) So, x(sec theta - tan theta) = 1Sec theta - tan theta = 1/xThus ,we have Sec theta + tan theta = x ----------(1)And, sec theta - tan theta =1/x -------(2)Now, Adding and subtracting these two equations we get, 2sec theta = X +1/x And, 2 tan theta = x-1/x So, sec theta = 1/2(x +1/x) And, tan theta =1/2(x-1/x)Now, Sin theta= tan theta/ sec thetaSo, sin theta = 1/2(x-1/x)/1/2(x + 1/x)=x^2 - 1/x^2 +1Hence proved