sec 38/cosec52 + 2/root3 *tan17*tan38*tan60*tan52*tan73-3(sin^2 32 + S

1.	sec 38/cosec52 + 2/root3 tan17tan38tan60tan52*tan73-3(sin^2 32 + Sin^2 58)
Answer» sec38/cosec52 + 2/√3(tan17tan38 tan60tan52tan73) - 3(sin²32 + sin²58). ⇒sec(90 - 52)/cosec52 + 2/√3{tan(90 - 73)tan73 tan(90 - 52) tan52 tan60} - 3{sin²(90 - 58) + sin²58}. we know :-sec(90 - Ф) = cosecФsin(90 - Ф) = cosФtan(90 - Ф) = cotФtan60 = √3let us apply here, ⇒cosec52/cosec52 + 2/√3 * (cot73 tan73 cot52tan52√3) - 3(cos²58 + sin²58) [ sin²A + cos²A ] ⇒1 + 2(1/tan73 * tan73 * 1/tan52 * tan52) - 3(1) ⇒1 + 2 - 3 ⇒3 - 3 = 0

sec 38/cosec52 + 2/root3 tan17tan38tan60tan52*tan73-3(sin^2 32 + Sin^2 58)

Answer»

sec38/cosec52 + 2/√3*(tan17tan38 tan60tan52tan73) - 3(sin²32 + sin²58).

⇒sec(90 - 52)/cosec52 + 2/√3*{tan(90 - 73)tan73 tan(90 - 52) tan52 tan60} - 3{sin²(90 - 58) + sin²58}.

we know :-sec(90 - Ф) = cosecФsin(90 - Ф) = cosФtan(90 - Ф) = cotФtan60 = √3let us apply here,

⇒cosec52/cosec52 + 2/√3 * (cot73 *tan73* cot52*tan52*√3) - 3(cos²58 + sin²58)

[ sin²A + cos²A ]

⇒1 + 2(1/tan73 * tan73 * 1/tan52 * tan52) - 3(1)

⇒1 + 2 - 3

⇒3 - 3 = 0