Question

If sec theta + tan theta = p show that sec theta - tan theta =1/p. Hence find the values of cos theta and sin theta.

Answer 1

sec@ + tan@ = p ———(1)
sec²@ – tan²@ = 1
(sec@ + tan@)×(sec@ – tan@) = 1
p×(sec@ – tan@) = 1
sec@ – tan@ = 1/p ——(2)

(1) + (2)
2 sec@ = (p+1/p) = (p²+1)/p
sec@ = (p²+1)/2p
cos@ = 2p/(p²+1)

(1) — (2)
2tan@ = p–1/p = (p²–1)/p
tan@ = (p²–1)/2p

tan@ ÷ sec@ = [(p²–1)/2p]÷[(p²+1)/2p]
sin@ = (p²–1)/(p²+1)

Answer 2

Answer:

Hope it helps you friend.