Math, asked by nandeswarinandu, 8 months ago

Prove that (1 + cot teta - cosec teta )(1 + tan teta + sec teta) = 2.​

Answers

Answered by adityaraj1756
2

Answer:

2. Ans.

Step-by-step explanation:

->LHS= [1+cos/sin-1/sin][1+1/cos+sin/cos]

= [cos+sin-1][cos+sin+1]/cos*sin

=[cos+sin]^2-(1)^2/cos*sin

=1+2cos•sin-1/cos•sin

now 1 and -1 will be cut down

=2cos•sin/cos•sin

cos•sin will cut down

= 2 ....Ans.

HOPE THIS WILL HELP YOU!

Answered by Anonymous
6

To Prove :

  • (1 + cot theta - cosec theta )(1 + tan theta + sec theta) = 2.

Solution :

LHS :(1 + cotØ - cosecØ)(1 + tanØ + secØ)

we know that,

  • cotØ = cosØ/sinØ
  • tanØ = sinØ/cosØ

  \rm \:  = (1 +  \frac{cos \:  \theta}{sin \: \theta}  -  cosec \:  \theta)(1 +  \frac{sin \:  \theta}{cos \:  \theta }+ sec \:  \theta)

  • cosecØ = 1/sinØ
  • secØ = 1/cosØ

  \rm \:  = (1 +  \frac{cos \:  \theta}{sin \: \theta}   -  \frac{1}{sin \:  \theta} )(1 +  \frac{sin \:  \theta}{cos \:  \theta} +  \frac{1}{cos \:  \theta})

\rm \:   = ( \frac{sin \:  \theta + cos \:  \theta - 1}{sin \:  \theta} )( \frac{cos \:  \theta + sin \: \theta + 1}{cos \:  \theta} )

\rm \:   = \frac{ \{(sin  \: \theta + cos \:  \theta) - 1 \}. \{(sin \:  \theta + cos \:  \theta) + 1 \}}{sin  \: \theta.cos \:  \theta}

\rm \:   =  \frac{{(sin \:  \theta + cos \:  \theta)}^{2}  - 1}{ sin \:  \theta.cos \: \theta}

\rm \:   =  \frac{{sin {}^{2}  \:  \theta + cos  {}^{2} \:  \theta + 2sin \: \theta \: cos \:  \theta} - 1}{ sin \:  \theta.cos \: \theta}

we know that,

  • sin²Ø + cos²Ø = 1

\rm \:   = \frac{1 + 2sin \theta \: cos \theta - 1}{sin \theta \: cos \theta}

\rm \:   = \frac{2 \cancel{sin \theta \: cos \theta}}{ \cancel{sin \theta \: cos \theta}}

= 2

Hence, Proved

━━━━━━━━━━━━━━━━━━━━━━━━━

Similar questions