Question

Show that :

(sec⊖ - tan⊖)² = 1-sin⊖/1+sin⊖

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Answer 1

✿ Qᴜᴇsᴛɪᴏɴ :-

Show that :

(sec⊖ - tan⊖)² = 1-sin⊖/1+sin⊖

✎ Sᴏʟᴜᴛɪᴏɴ :-

(sec⊖ - tan⊖)² = [1/cos⊖ - sin⊖/cos⊖]²

= [1-sin⊖/cos⊖]² = (1 - sin⊖)²/cos²⊖

= (1-sin⊖)²/1-sin²⊖ = (1-sin⊖)(1-sin⊖)/(1-sin⊖)(1+sin⊖)

= 1-sin⊖/1 + sin⊖

Answer 2

= (1-sin⊖)²/1-sin²⊖ = (1-sin⊖)(1-sin⊖)/(1-sin⊖)(1+sin⊖)

= 1-sin⊖/1 + sin⊖