Question

Prove that :(1) sin 60° cos 30°+ cos 60° sin 30°= 1
(2) 3 cosec ²60° - 2cot square 2 30° + Sec square2 45°=0​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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Solution:

1 ) sin 60° cos 30° + cos 60° sin 30° = 1

$\sf = \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2} + \dfrac{1}{2} \times \dfrac{1}{2}$

$\sf = { \huge (}{ \dfrac{ \sqrt{3} }{2} { \huge)}}^{2} + { \huge(} {\dfrac{1}{2}} { \huge)}^{2}$

$\sf = \dfrac{3}{4} + \dfrac{1}{4}$

$\sf = \dfrac{3 + 1}{4}$

$\sf = \dfrac{4}{4}$

$\sf = 1$

Hence Proved!!

2) 3 cosec² 60° - 2 cot² 30° + sec² 45°= 0

$\sf = 3 \times{ { \huge(} \dfrac{ 2 }{ \sqrt{3} } { \huge)} }^{2} - 2 \times { (\sqrt{3} )}^{2} + { (\sqrt{2} )}^{2}$

$\sf = 3 \times \dfrac{4}{3} - 2 \times 3 + 2$

$\sf = \cancel3 \times \dfrac{4}{ \cancel3} - 6 + 2$

$\sf = 4 - 6 + 2$

$\sf = 6 - 6$

$\sf = 0$

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