Question

sin theta + cos theta upon sin theta minus cos theta + sin theta minus cos theta upon sin theta + cos theta equal to 2 sec square theta upon tan square theta minus one​

Answer 1

Answer:

ꜱɪɴθ+ᴄᴏꜱθ=ᴩ.............................(1)

ᴛᴀɴθ+ᴄᴏᴛθ=q.............................(2)

ꜱqᴜᴀʀɪɴɢ ᴏɴ ʙᴏᴛʜ ꜱɪᴅᴇꜱ ᴏꜰ (1),

ꜱɪɴ2θ+ᴄᴏꜱ2θ+2ꜱɪɴθᴄᴏꜱθ=ᴩ2

⇒ꜱɪɴ2θ=ᴩ2−1

⇒ᴄꜱᴄ2θ=ᴩ2−11..........(3)

ꜰʀᴏᴍ (2), 

        ᴛᴀɴθ+ᴛᴀɴθ1=q

        2ᴛᴀɴθᴛᴀɴ2θ+1=2q

        ᴄꜱᴄ2θ=2q........(4)

ꜰʀᴏᴍ (3) ᴀɴᴅ (4),

              ᴩ2−11=2q⇒(ᴩ2−1)q=2

ʜᴇɴᴄᴇ, 2 ɪꜱ ᴛʜᴇ ʀɪɢʜᴛ ᴀɴꜱᴡᴇʀ.