Question

${\huge{\red{\underline{\bold{QuestioN↑}}}}}$

ʙᴏᴀʀᴅ- ɪᴄsᴇ 10
______________
• sᴏʟᴜᴛɪᴏɴ sʜᴏᴜʟᴅ ʙᴇ ᴄʟᴇᴀʀ ᴀɴᴅ ɪᴛ ɪs ᴀʙʟᴇ ᴛᴏ ᴜɴᴅᴇʀsᴛᴀɴᴅ.

• ɴᴏ ғᴀʟᴛᴜ ᴀɴsᴡᴇʀs ᴛᴏ ʙᴇ ɢɪᴠᴇɴ.

• ᴄᴏʀʀᴇᴄᴛ sᴏʟᴜᴛɪᴏɴ ᴡɪʟʟ ʙᴇ ᴍᴀʀᴋ ʙʀᴀɪɴʟɪᴇsᴛ ᴀɴᴅ 50 ᴛʜᴀɴᴋs ᴛᴏ ʜɪs/ʜᴇʀ ᴀɴsᴡᴇʀs.​

Answer 1

= sin2 34˚ + cos2 (90˚ – 56˚) + 2 tan 18˚ cot(90˚ – 72˚) – (√3)2

= (sin2 34˚ + cos2 34˚) + 2 tan 18˚ × 1/tan 18˚ – 3

= 1 + 2 – 3 = 3 – 3 = 0

Answer 2

$\bf{ \orange{ ={ \sin}^{2} 34 \degree + { \sin}^{2} 34 \degree + 2 \tan18 \degree \tan72 \degree - { \cot}^{2} 30 \degree }}$

$\bf{\pink {={ \sin }^{2}34 + [ \sin(90 \degree - 34 \degree ] {}^{2} + 2 \tan18 \degree \tan(90 \degree - 18 \degree) - { \cot}^{2} 30 \degree }}$

$\bf{ \red{= { \sin }^{2} 34 + { \cos}^{2}34 \degree + 2 \tan18 \degree \cot18 \degree - ({ \sqrt{3}) }^{2} }}$

$\bf{ \green{ = 1 + 2 \tan18 \degree \times \frac{1}{ \tan18 \degree } - 3 }}$

$\bf{ \purple{ = 1 + 2 \: \cancel{\tan18 \degree} \times \frac{1}{ \cancel{ \tan18 \degree }} - 3 }}$

$\bf{ \blue{ = 1 + 2 - 3 = 0}}$

$\bf{hence \: value \: is \: \red0.}$